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Is it what you say or how you say it?

Published online by Cambridge University Press:  14 March 2025

Xiangdong Qin
Affiliation:
Department of Economics, Shanghai Jiao Tong University, Shanghai, China
Siyu Wang*
Affiliation:
Department of Economics and Institute for the Study of Economic Growth, Wichita State University, Wichita, USA
Mike Zhiren Wu
Affiliation:
Department of Economics, Monash University, Melbourne, Australia
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Abstract

This study investigates the mechanisms driving the effectiveness of free-form communication in promoting cooperation within a sequential social dilemma game. We hypothesize that the self-constructing nature of free-form communication enhances the sincerity of messages and increases the disutility of dishonoring promises. Our experimental results demonstrate that free-form messages outperform both restricted promises and treatments where subjects select and use previously constructed free-form messages. Interestingly, we find that selected free-form messages and restricted promises achieve similar levels of cooperation. We observe that free-form messages with higher sincerity increase the likelihood of high-price and high-quality choices, thereby promoting cooperation. These messages frequently include promises and honesty, while threats do not promote cooperation. Our findings emphasize the crucial role of the self-constructed nature of free-form messages in promoting cooperation, exceeding the impact of message content compared to restricted communication protocols.

Type
Original Paper
Creative Commons
Creative Common License - CCCreative Common License - BY
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Copyright
Copyright © The Author(s) 2024

1 Introduction

Communication plays a pivotal role in human interactions, especially those requiring cooperation between individuals. Both economists and psychologists have a long-standing interest in the impact of free-form communication on decision-making. Economists tend to adopt a generalized and abstract approach, using comparisons of communication protocols to quantify the effect of communication and focusing on the resulting changes in outcomes (e.g., Bornstein & Rapoport Reference Bornstein and Rapoport1988; Bochet et al. Reference Bochet, Page and Putterman2006; Charness & Dufwenberg Reference Charness and Dufwenberg2006; Cooper and Kühn Reference Cooper and Kai-Uwe2014). In contrast, the psychology literature includes remarkable works that explore the intricate nuances of language and meaning, especially with respect to the conveyance of probabilistic information (e.g., Budescu & Wallsten Reference Budescu and Wallsten1985; Reference Budescu and Wallsten1995; Wallsten et al. Reference Wallsten, Budescu, Rapoport, Zwick and Forsyth1986; Reference Wallsten, Budescu and Zwick1993), uncertainties (Budescu et al., Reference Budescu, Weinberg and Wallsten1988; von Furstenberg & Wallsten, Reference von Furstenberg and Wallsten1990), and fuzzy reasoning (Zwick et al., Reference Zwick, Carlstein and Budescu1987).

This study aims to deepen our comprehension of the effectiveness of natural language communication in fostering cooperation by drawing inspiration from both of these perspectives. We share with other scholars a curiosity about the nuances of communication while focusing on generality in our approach. In line with the rationales proposed by Ellingsen and Johannesson (Reference Ellingsen and Johannesson2004) and Vanberg (Reference Vanberg2008), which are respectively based on lying aversion and guilt aversion, we propose a novel framework to explain why free-form communication may be even more effective than restricted promises. We hypothesize that individuals display more sincerity when constructing messages using their own words, which increases the disutility associated with disappointing others and thereby reinforces the effectiveness of free-form communication in fostering cooperation. Our hypothesis resonates with findings in psychology, which suggest that people are more inclined to engage in socially desirable actions when their sense of self is involved, as indicated by research from Bryan et al. (Reference Bryan, Walton, Rogers and Dweck2011, Reference Bryan, Adams and Monin2013) and Chou (Reference Chou2015).

To test this idea, we conducted a sequential social dilemma game where buyers set prices for their goods and sellers determine the quality of the goods. We introduced five treatments: a baseline without communication, restricted promises, restricted threats, free-form communication, and a message-select treatment where messages are chosen from pre-constructed free-form options. In all communication treatments, the seller can send a costless, nonbinding message to the buyer before the dilemma begins.

This design allows us to explore factors that contribute to the differing effectiveness of free-form and restricted messages. We consider two plausible explanations. First, the richness of natural language may enhance the effectiveness of free-form communication. If this is the case, the message-select treatment should surpass the restricted promise treatment in effectiveness. Alternatively, the inherent sincerity of self-constructed free-form messages might be the key, regardless of message content. If this holds true, the free-form message treatment should outperform both the message-select and restricted promise treatments.

Our experimental findings indicate that free-form communication significantly outperforms all restricted communication treatments in terms of promoting cooperation. The message-select treatment performs as effectively as the restricted promise treatment but falls significantly short of free-form communication, highlighting the crucial role of self-constructed messages. In both the message-select and free-form treatments, we frequently observed the inclusion of promise and honesty notions. Interestingly, these notions appear more effective in promoting cooperation when they are part of free-form messages. Additionally, our analysis reveals that the restricted promise treatment is more conducive to cooperation compared to the restricted threat treatment. A notable aspect of these findings is the persistence of treatment differences in cooperative behavior, as evident from both the senders and receivers of messages. This suggests that both parties are aware of the varying levels of sincerity associated with different communication forms and their potential impact on cooperative outcomes. With additional evaluation sessions that rated the sincerity of the messages, we observed that messages with higher sincerity increase the likelihood of both high-price and high-quality choices, thereby promoting cooperation.

As emphasized by Rubinstein (Reference Rubinstein2000),Footnote 1 “Economic theory is an attempt to explain regularities in human interaction, and the most fundamental nonphysical regularity in human interaction is natural language.” Economists strive to simplify human interaction as a structured decision-making process. However, real-life interactions, especially those in daily conversations, predominantly use natural language and thus introduce numerous complexities that are difficult to represent effectively within simplified economic models.

Consistent with the methodology of Rapoport and coauthors (e.g., Kahan & Rapoport, Reference Kahan and Rapoport1984; Rapoport, Reference Rapoport2012), this study combines game-theoretical models with experimental research to understand decision-making processes in the context of natural language complexity. We use meticulously designed experiments to enhance our understanding of the effectiveness of natural language communication in promoting cooperation.

The rest of the paper is organized as follows. Section 2 provides a brief overview of the relevant studies on communication. Section 3 outlines our experimental design, and Sect. 4 presents the behavioral model and hypotheses. Section 5 presents the main findings, and Sect. 6 concludes the paper.

2 Related literature

2.1 Cheap talk

In the communication literature, pre-play “cheap talk” (i.e., non-binding, non-verifiable communication) is repeatedly shown to outperform many other mechanisms in resolving coordination or cooperation failures (e.g., Brandts & Cooper Reference Brandts and Cooper2007; Duffy & Feltovich Reference Duffy and Feltovich2002). In a large-scale meta-analysis of 130 distinct experiments from 37 studies, Sally (Reference Sally1995) finds that communication is the most effective mechanism for solving social dilemmas such as the public goods game and the prisoner's dilemma.

Economists are greatly interested in a theoretical understanding of the potential importance of cheap talk. Early studies in this area focus on whether pre-play communication can facilitate equilibrium play. For instance, Farrell (Reference Farrell1987) discusses how cheap talk can foster asymmetric coordination in an entry game and offers the following logic: if players’ announced plans constitute a Nash equilibrium, then this equilibrium would become focal and be followed by both players, thus reducing the frequency of ex-post disequilibria. Rabin (Reference Rabin1994) extends the analysis of Farrell (Reference Farrell1987) to unlimited rounds of communication. In his model, the players make repeated, simultaneous statements about their intended actions before playing a coordination game; if this communication between players is sufficiently long, each player should perform at least slightly better than her worst Pareto-efficient Nash equilibrium.

The analyses by Farrell (Reference Farrell1987) and Rabin (Reference Rabin1994) provide a useful benchmark for evaluating the effectiveness of cheap talk. Their arguments are supported by several follow-up experimental studies in which cheap talk is shown to increase both the incidence of equilibrium play and the frequency of efficient equilibria. For example, Cooper et al. (Reference Cooper, DeJong, Forsythe and Ross1989) investigate the effect of communication in the Battle of the Sexes game. They find that communication significantly increases the frequency of equilibrium play, as the players can indicate their planned actions using cheap talk messages. Duffy and Feltovich (Reference Duffy and Feltovich2002) find that one-way cheap talk results in increased coordination via a pure Nash equilibrium and thus increases efficiency. Blume and Ortmann (Reference Blume and Ortmann2007) study minimum and median games with Pareto-ranked equilibria in which multiple players can send numerical messages to signal their intended choices. Their results show that cheap talk increases coordination with a Pareto-efficient equilibrium.

However, no consensus exists regarding the effectiveness of pre-play communication for achieving efficient outcomes. Aumann (Reference Aumann1990) expresses doubt that cheap talk can enhance trust and promote efficiency in a stag hunt game, given that the intention to cooperate during a hunt is self-serving: each player strictly prefers to tell others to cooperate, regardless of her own intention. However, Charness (Reference Charness2000) shows experimentally that even self-serving cheap talk can facilitate coordination to achieve an efficient equilibrium, provided that the signaling stage precedes the action stage.

Increasingly, studies are exploring why cheap talk increases the efficiency of outcomes. Conventionally, scholars invoke behavioral heuristics to explain the effectiveness of communication. For example, Ellingsen and Johannesson (Reference Ellingsen and Johannesson2004) argue that people's concerns about fairness and consistency drive them to follow through on their commitments. Charness and Dufwenberg (Reference Charness and Dufwenberg2006) offer a similar perspective, positing that players are guilt-averse and thus wish to avoid failing to fulfil their commitments to others. Vanberg (Reference Vanberg2008) revisits the game of Charness and Dufwenberg (Reference Charness and Dufwenberg2006) and proposes that the result is driven not by guilt aversion but rather by an intrinsic preference for promise-keeping. Lying aversion, defined as a person's intrinsic motivation to maintain the credibility of their communications, is another common behavioral explanation for the effectiveness of cheap talk (Charness & Dufwenberg, Reference Charness and Dufwenberg2010; Ellingsen & Östling, Reference Ellingsen and Östling2010; Lundquist et al., Reference Lundquist, Ellingsen, Gribbe and Johannesson2009). Fehrler et al. (Reference Fehrler, Fischbacher and Schneider2020) find that while promises increase transfers between subjects, the credibility of a statement crucially depends on participants’ self-selection into cheap-talk situations.

2.2 Comparison of communication protocols

The economics literature compares various channels and structures of communication to determine the effectiveness of different communication protocols (see, e.g., Brandts et al., Reference Brandts, Cooper and Rott2019). Experimental evidence suggests that these protocols vary in terms of effectiveness. For example, Bochet et al. (Reference Bochet, Page and Putterman2006) find that efficiency in a public goods game increases markedly with communication via a chat room but does not increase with numerical communication via computer terminals. Similarly, in a collective resistance game, Cason and Mui (Reference Cason and Mui2015) observe a higher level of coordination when rich communication is used than when simultaneous intention signals are used. Ben-Ner et al. (Reference Ben-Ner, Putterman and Ren2011) compare two types of communication in a trust game: a single-round exchange of numerical proposals by a trustor and trustee, and a combination of proposal exchanges and unrestricted free chats. The authors find that although both kinds of communication facilitate trust and trustworthiness, verbal communication has a stronger effect than numerical signals. Charness and Dufwenberg (Reference Charness and Dufwenberg2006, Reference Charness and Dufwenberg2010) find that written free-form promises increase trust and trustworthiness significantly in a one-shot trust game with hidden actions. In contrast, the use of a pre-designed “bare promise” message (for example, “I promise to choose ‘Roll’ ”) only moderately enhances trustworthiness. Lundquist et al. (Reference Lundquist, Ellingsen, Gribbe and Johannesson2009) provide evidence that free-form messages lead to fewer lies than do pre-formulated promises in a hiring game with one-sided information asymmetry. In their experiment, the participants first perform a real-effort task to determine their skill, which is private information. They are then matched and play a one-shot game in which the applicant first signals her ability and the employer decides whether to offer a contract. The authors find that the proportion of low-skill applicants who over-report their abilities is significantly higher under the treatment with pre-formulated messages than under the treatment with free-form messages. Cooper and Kühn (Reference Cooper and Kai-Uwe2014) investigate how various communication types may foster cooperation in a two-stage collusion game. They find free-form chat to be the most effective communication method, especially when threats are involved. Moreover, they find that communication via a limited message space is not a good substitute for natural conversation.

2.3 What makes free-form communication more effective?

Ample evidence supports the superior efficacy of free-form communication compared with restricted messages, prompting researchers to investigate the underlying mechanisms of this efficacy. Experimental studies conducted across different environments offer explanations centering around distinct factors.

A group of existing research highlights the relationship-building function of free-form communication. A notable example comes from Mohlin and Johannesson (Reference Mohlin and Johannesson2008), where researchers attempted to explain the increased donation amounts in a standard dictator game when the recipient sends free-form messages. They designed a third-party communication treatment to isolate the content effect of free-form messages while eliminating the relationship-building effect. The authors find that the contributions from the relationship effects are comparable to the content effect in facilitating effective communication. In a study by Coffman and Niehaus (Reference Coffman and Niehaus2020), the focus is on a sales setting where sellers engage in free-form conversation to persuade buyers to increase their valuations of objects. They examine two pathways of persuasion: appealing to the buyer's self-interest and building rapport. The results show that sellers more frequently target buyers’ self-interest, and changes in self-interest explain a significant portion of persuasion. However, sellers are found to be most persuasive when they focus on rapport building.

The ability of free-form messages to facilitate type detection has also been extensively discussed in previous studies. In He et al. (Reference He, Offerman and Van De Ven2017), the authors explore the factors influencing the effectiveness of face-to-face communication in resolving social dilemmas. They tested several possible channels, and type detection is identified as playing a key role in increasing cooperation. The research also emphasizes the freedom to create promises in communication, as it not only enhances the commitment value but also aids in revealing the type. In a study by Ismayilov and Potters (Reference Ismayilov and Potters2016), the aim is to understand whether promise-making (internal consistency) or promise-receiving (social obligation) can explain the effect of promises on trustworthiness. The results of that study indicate that promises do not directly induce trustworthiness; rather, promises are important in signaling types, being more likely to be made by cooperators than non-cooperators. Turmunkh et al. (Reference Turmunkh, Van den Assem and Van Dolder2019) investigate the credibility of nonbinding pre-play statements about cooperative behavior using data from a high-stakes TV game show. To better understand the messages, they propose a two-by-two typology focusing on the conditionality and implicitness. The assumption of lying aversion is introduced, where potential defectors prefer statements that can be interpreted later as true. The authors’ analysis shows a link between statements with conditionality or implicitness and a reduced likelihood of cooperation, suggesting that malleability is a reliable criterion to differentiate types.

Additionally, there is a small but growing literature using the richness of free-form messages as an explanation for the effectiveness of free-form communication. Dugar and Shahriar (Reference Dugar and Shahriar2018) conduct stag hunt games to understand the efficiency-enhancing capacities of various types of messages. While intentional signaling messages fail to facilitate cooperation, the ineffectiveness of such messages can be ameliorated by adding reason-based components. Notably, the reason-based messages are found to be an effective efficiency-enhancing device similar to free-form messages. Therefore, Dugar and Shahriar (Reference Dugar and Shahriar2018) posit that the effectiveness of free-form communication can be explained by the sender's ability to specify the reason for choosing the cooperative behavior. Wang and Houser (Reference Wang and Houser2019) use a pure coordination game to examine differences in effectiveness between communication via intention signaling and communication via natural language. Free-form messages in this environment are found to include both signaled intentions and attitudes (i.e., the strength of a message sender's desire to have her message followed), and people respond to both intentions and attitudes when making decisions. The study finds that the difference in attitudes improves coordination significantly as the player indicating a weaker intention yields to the player indicating a stronger intention.

The psychology literature suggests that people are more inclined to engage in socially desirable behavior when their sense of self is evoked. This concept is rooted in the understanding that individuals often strive to maintain a positive self-image and are thus influenced by how their actions align with their personal identity. For example, Bryan et al. (Reference Bryan, Adams and Monin2013) provided participants with an opportunity to claim unearned money at the experimenters’ expense, using instructions that highlighted the identity implications of cheating (e.g., “Please don’t be a cheater”) versus focusing on the action (e.g., “Please don’t cheat”). The study found that participants in the “cheating” condition claimed more money than those in the “cheater” condition, a pattern evident in both face-to-face and online settings. This outcome suggests the power of language in influencing ethical behavior by appealing to individuals’ desire to maintain a positive self-image. Similarly, Bryan et al. (Reference Bryan, Walton, Rogers and Dweck2011) examined the impact of framing survey items to reflect a personal identity (e.g., “being a voter”) versus merely describing a behavior (e.g., “voting”). This study revealed that identity-based framing significantly increased voter registration and turnout, as evidenced by state records. These results highlight the role of self-concept management in motivating socially desirable actions. Chou (Reference Chou2015) investigated the effectiveness of various electronic signatures in comparison to handwritten signatures in deterring dishonesty. The study's findings across seven experiments consistently showed that electronic signatures are less effective in curbing dishonest behavior. This ineffectiveness is linked to their inability to evoke a sense of self-presence in the signer. Meta-analyses further established the reliability of these associations, emphasizing the role of self-presence in ethical decision-making. These studies collectively show that when the self identity is evoked, individuals are more likely to behave in ways that are congruent with their values and societal norms. This tendency to act in a manner that preserves a positive self-concept can significantly shape behavior, particularly in contexts where ethical or moral decisions are involved.

The focus of our work is closely related to the last two strands of literature. To understand the difference in effectiveness between free-form messages and restricted messages, we consider both the role played by the richness of natural language and the self-constructed nature of the messages.

3 Experimental design

3.1 Sequential social dilemma

We design a sequential social dilemma game involving two players: a seller and a buyer. In the game, the buyer takes initiative and offers a price, which can be either high ( P H ) or low ( P L ). Based on this offer, the seller then decides whether to provide a high-quality ( Q H ) or low-quality ( Q L ) product.

Both the buyer's evaluation of the product, denoted as V(Q), and the production cost, denoted as C(Q), increase with the quality of the product. Specifically, higher-quality products are of higher value to the buyer and impose higher production costs on the seller. To introduce a social dilemma element, we carefully selected the following set of parameters for our experiment: V ( Q H ) = 300 , V ( Q L ) = 100 ; P H = 200 , P L = 50 ; C ( Q H ) = 100 , C ( Q L ) = 0 .

In the game, the buyer's payoff is calculated as the difference between the value of the product and the price offered, while the seller's payoff is derived from the difference between the price and the production cost.

Fig. 1 The sequential social dilemma game

Figure 1 presents the game tree, wherein a unique subgame perfect Nash equilibrium is achieved when the buyer proposes a low price and the seller, in response, provides a low-quality product. However, an opportunity for Pareto improvement exists if the buyer decides to offer a high price and, as a result, receives a high-quality product. This framework allows the examination of communication dynamics and their impact with respect to enhancing outcomes between the buyer and the seller across different treatments.

3.2 Communication treatments

Under the baseline treatment, the sequential social dilemma is conducted without any communication between the buyer and the seller. To compare the effects of free-form messages with those of restricted protocols, we introduce different communication treatments. Under these treatments, the seller is allowed to send a free, non-binding message to the buyer before the dilemma game begins. For this experiment, we designed four communication treatments that vary in terms of the form of the messages exchanged between the buyer and the seller.

Beginning with restricted messages, the restricted promise treatment allows the seller to choose between sending a restricted form of a promise, stating “If you pay a high price, I will choose high quality,” or leaving the message blank. Under the restricted threat treatment, the seller can choose to send a restricted form of a threat, stating “If you pay a low price, I will choose low quality,” or leaving the message blank.

Under the free-form communication treatment, the seller has complete freedom to write messages without any constraints on the number of words or message length.

Under the message-select treatment, the sender can choose from a list of 10 randomly selected messages crafted by sellers during the free-form communication treatment sessions, or leaving the message blank. Here, the richness of language in the message space (as analyzed in Sect. 5.4) is similar to that used under the free-form treatment, but the factor of message self-construction by the sender is removed. This allows us to isolate the effects of self-construction and message content richness that contribute to the differences in persuasiveness between restricted and free-form messages.

In all four communication treatments, we ensured that buyers were fully informed about the nature of the messages, whether they were selected from a pool or constructed by the sellers themselves. Under the two treatments with restricted messages, the buyer is fully informed about the messages available to the seller. Under the free-form treatment, the buyer is aware that the seller is free to write anything. Under the message-select treatment, the buyer is aware that the seller's messages are chosen from a set of previously constructed options. However, the buyer is not provided with the explicit set of messages available to the seller. For the message-select treatment, the available message options were limited to a pool collected from the free-form treatment. To balance variety with manageability, we provided a list of 10 randomly selected messages, aiming to avoid overwhelming subjects with an excessive number of choices. This approach, however, may have introduced potential bias, as subjects might not have found messages that precisely matched their intended communication. Nevertheless, this limitation is further discussed in the results section, where we compare the content delivered in free-form and message-select treatments, and their effectiveness.

By comparing the differences between treatments, we can also effectively study the prevalence of cooperation failure under the baseline treatment and replicate previous findings that free-form messages tend to better promote cooperation than do restricted messages. Furthermore, this design enables us to deepen our insights into the dynamics of free-form and restricted communications and their respective impacts on cooperation outcomes.

3.3 Experimental details

The experiment took place at the Smith Experimental Economics Research Center, Shanghai Jiao Tong University, in November and December 2019 and November 2020.Footnote 2 The z-Tree program was used to conduct the experiment. Details regarding the numbers of sessions and participants per treatment can be found in Table 1. Overall, the experiment involved 354 participants, none of whom had prior experience with similar studies.

Table 1 Summary of the treatments

Treatment

Number of sessions

Number of subjects

Baseline

3

70

Restricted threat

3

70

Restricted promise

3

70

Message-select

3

72

Free-form

3

72

Total

15

354

We adopted a between-subject design wherein each subject experienced only one treatment. Before experiencing the treatment, the subjects were provided with printed instructions. To ensure better comprehension, a recording of the instructions was played aloud. The detailed instructions can be found in Appendix 3.

Under each treatment, the game was played repeatedly for 10 rounds. We used stranger matching to pair the subjects and assigned their roles randomly. Under the message-select treatment, the list of messages was re-selected randomly during each round and varied across the sessions.

To ensure a non-negative payoff, both the seller and the buyer were provided with 100 tokens at the beginning of each round. After each round, the players were informed of their counterpart's actions and earnings during that round. To prevent the players from hedging their bets across different rounds, payments were made only during one randomly selected round (for more details, see the discussion in Azrieli et al., Reference Azrieli, Chambers and Healy2018).

Upon the conclusion of the experiment, we collected additional information from the subjects, including their demographics and risk preferences, which were assessed using the method proposed by Crosetto and Filippin (Reference Crosetto and Filippin2013). In addition, we examined their social preferences as part of the data collection process.Footnote 3

The experimental sessions lasted approximately one hour on average. The subjects’ average accumulated earnings were 56.18 RMB. This amount includes a 15 RMB show-up fee. The U.S. dollar/Chinese yuan (RMB) exchange rate during the experiment ranged from approximately 6.54 to 7.07.

4 Theoretical framework and hypotheses

To offer predictions and rationale for the effect of communication in our experiment, we present a straightforward theoretical framework. In this framework, we introduce the concept of sincerity as denoted by S, which reflects the perceived persuasiveness of a statement. Both the seller and the buyer are assumed to share a transitive ordering for sincerity . For simplicity, we let S { 0 , 1 , 2 , , N } , with larger values in the set indicating higher degrees of sincerity .

4.1 The seller's problem

We assume that the seller incorporates both material interest and psychological costs into his utility function:

max S , Q U S = P - C ( Q ) - θ · S · ψ ( P , Q ) - ω · χ ( S , Q )

where ψ ( P , Q ) = 1 i f P = P H a n d Q = Q L 0 o t h e r w i s e , χ ( S , Q ) = 1 i f S > 0 a n d Q = Q L 0 o t h e r w i s e

There are two psychological forces at play in this context. The first force, guilt aversion, is represented quantitatively as θ · S · ψ ( P , Q ) . Here, ψ ( P , Q ) is a binary variable that takes a value of 1 if the sender fails to meet the buyer's expectations, and 0 otherwise. In the game, this occurs when the buyer offers a high price but receives a low-quality product, leading the seller to experience a disutility level of θ · S . The parameter θ reflects the seller's sensitivity toward guilt and can take one of two values: θ H or θ L , where θ H is greater than θ L . Both players share a common prior, denoted as p ( θ H ) . The parameter S denotes sincerity , which reflects the perceived persuasiveness of a statement.

The second force, aversion to lying, is denoted as ω · χ ( S , Q ) . Here, χ ( S , Q ) is a binary variable that takes a value of 1 if and only if the seller signals positive sincerity but ultimately supplies a low-quality product, irrespective of the buyer's choice. In such cases, a lying cost of ω is incurred.

4.2 The buyer's problem

After receiving the seller's message and detecting sincerity , the buyer forms her belief about the seller's type as μ ( θ | S ) (referred to as r S hereafter) and then chooses a price that maximizes her expected utility:

max P U B = θ μ ( θ | S ) · ( V ( Q θ ( S , P ) ) - P )

Q θ ( S , P ) represents the seller's optimal quality decision. For the analysis, we adopt the pure-strategy perfect Bayesian equilibrium as the solution concept.

We introduce two additional assumptions. First, following the approach of Ellingsen and Östling (Reference Ellingsen and Östling2010), we assume that the buyer possesses a weak lexicographic preference for being kind, such that P H P L when the buyer is indifferent. This assumption implies that we can always specify the buyer's exact choice. Second, we assume that the difference between the guilt sensitivity of the two types is significantly large, such that θ H > C ( Q H ) - C ( Q L ) - ω > θ L > 0 .

4.3 Equilibrium analysis

In this subsection, we discuss the equilibrium analysis for various communication protocols. These protocols differ primarily in the sincerity S of the messages that they permit. A detailed proof of the equilibrium analysis can be seen in Appendix 2.

Restricted Promise: Consider S { 0 , 1 } , where S = 1 if the seller chooses to send a restricted promise and S = 0 if the seller sends an empty talk. In this case, the optimal strategy profile on quality is:

Q θ ( S , P ) = Q H i f P = P H , S = 1 , θ = θ H Q L o t h e r w i s e

There are two pooling equilibria in this scenario. In the first equilibrium, both types pool on S = 0 , and the buyer's best response is P L , regardless of the received message, when r 0 [ 0 , 3 4 ) . Consequently, both types of sellers respond according to Q θ ( S , P ) and play Q L . This is the empty-talk equilibrium.

In the second equilibrium, both types of sellers pool on S = 1 , and the buyer always chooses to trust,Footnote 4 selecting P H if the prior p ( θ H ) ( 3 4 , 1 ] . Consequently, cooperation ( P H , Q H ) can be achieved between a seller of type θ H and the buyer, whereas a seller of type θ L chooses to betray the buyer's trust. This is the limited sincerity pooling equilibrium.

Message-select: Let us consider S { 0 , 1 , . . . , N } where N is not sufficiently large, such that C ( Q H ) - C ( Q L ) - ω θ L > N 2 . In this case, the seller must choose between using empty talk or sending messages with limited but distinguishable levels of sincerity ( S > 0 ). Here, the seller's optimal quality decision is

Q θ ( S , P ) = Q H i f P = P H , S > 0 , θ = θ H Q L o t h e r w i s e

In this scenario, the equilibria are qualitatively similar to restricted promise communication. We observe an empty talk equilibrium and multiple limited sincerity pooling equilibrium where S θ H = S θ L = α for all values of α in the range N α > 0 . Similarly, cooperation ( P H , Q H ) can only be achieved between a seller of type θ H and the buyer in those limited sincerity pooling equilibria.

Free-form Communication: Consider S { 0 , 1 , . . . , N } , where N is sufficiently large: N k > 2 such that

1 + C ( Q H ) - C ( Q L ) - ω θ L > k > C ( Q H ) - C ( Q L ) - ω θ L

There exist some statements that are sufficiently sincere ( S k ) that even a seller of type θ L keeps their promise. Here, the seller's optimal quality decision is

Q θ H ( S , P ) = Q H i f P = P H , S > 0 Q L o t h e r w i s e Q θ L ( S , P ) = Q H i f P = P H , S k Q L o t h e r w i s e

In this case, in addition to the multiple limited sincerity pooling equilibria wherein S in k - 1 > S > 0 , there are two other types of equilibria where both types of sellers cooperate with the buyer.

The first type is the high sincerity pooling equilibrium, where both types of sellers tend to pool on highly sincere statements. Here, S θ H = S θ L = α for all values of α in the range N α > k . The buyer's best response is P H , given N S k , and P L otherwise. Both types of sellers ultimately achieve ( P H , Q H ) .

The second type is the high sincerity separating equilibrium, where the two types of sellers send different highly sincere statements. In this equilibrium, N S θ H = α k , N S θ L = β k , where α and β are distinct. Similarly, the buyer's best response is P H , given N S k , and P L otherwise. Both types of sellers can achieve ( P H , Q H ) in this equilibrium.

Restricted Threat: In our framework, sincerity is linked to the psychological costs associated with guilt aversion and aversion to lying. This suggests that messages intended to promote cooperative behavior should signal positive intentions or show a certain level of commitment. However, the restricted threat that a sender can employ, which underscores the non-cooperative outcome ( P L , Q L ), lacks such a commitment. Consequently, it's reasonable to assume that S = 0 in scenarios involving this kind of threat. Therefore, in treatments with a restricted threat, we expect that both sellers and buyers will exhibit behavior similar to what is observed in the baseline scenario.

4.4 Hypotheses

The theoretical framework and equilibrium analysis provide directional hypotheses for the experiment.

Hypothesis I

Cooperation is more likely under the restricted promise, message-select, and free-form treatments than under the baseline treatment.

Limited sincerity pooling equilibria clearly exist in all three communication cases analyzed. Thus, when involving a promise, these three communication treatments would result in more cooperation than a treatment where communication is not allowed (i.e., the baseline).

Hypothesis II

The cooperation rate is higher under the free-form treatment than under the restricted promise and message-select treatments.

According to the equilibrium analysis, a seller of type θ H always cooperates when offered a high price in the game, whereas a seller of type θ L only cooperates when the message is sufficiently sincere. Consequently, cooperation is more likely to occur when the communication contains a sufficiently high level of sincerity than when the sincerity level is insufficiently high. We assume that both the restricted promise treatment and the message-select treatment exhibit an insufficient level of sincerity. Conversely, under the free-form treatment, the seller has the freedom to write messages with a sufficiently high level of sincerity. We further investigate the validity of this assumption through an analysis of the experimental data.

Hypothesis III

The restricted threat treatment does not lead to a higher cooperation rate than the baseline treatment.

Given that no commitments or positive signals are conveyed when the seller issues a threat, it involves no psychological cost. Consequently, we hypothesize that the players’ choices under the restricted threat treatment will be comparable to those in the baseline treatment.

5 Results

5.1 Overview

We first present an overview of our comparison of treatments and cooperation levels to correspond with our hypotheses. Then, we explore the high price and high quality choices respectively.

RESULT 1a : The restricted promise, message-select, and free-form treatments have higher cooperation rates than the baseline treatment.

RESULT 1b: The cooperation rate is higher under the free-form treatment than under the restricted promise and message-select treatments.

RESULT 1c : The cooperation rate is not significantly different between the restricted promise and message-select treatments.

RESULT 1d : The cooperation rate is not significantly different between the restricted threat treatment and the baseline treatment.

Fig. 2 Distribution of outcomes

Figure 2 displays the distribution of outcomes as a result of each treatment. Our findings indicate that the effects of the baseline and restricted threat treatments are not significantly different, whereas the three treatments with promise opportunities outperform the baseline treatment. Notably, the message-select treatment promotes cooperation as effectively as the restricted promise treatment, but both are less effective than the free-form treatment.

Across all treatments, the most common outcomes are low price–low quality and cooperation on high price–high quality. Less than 2% of the paired players choose low price–high quality.

Statistical support for RESULT 1 (a–d) can be found in Table 2, where we present pairwise comparisons of cooperation under each treatment. Each cell in the table displays the marginal effect and clustered standard error obtained from one regression. We conduct probit regressions of cooperation on treatment dummies for which the dependent variable is cooperation, taking a value of 1 if the buyer and seller coordinate on high price–high quality and 0 otherwise. The main independent variable is the treatment, with the round fixed-effects being controlled. As cooperation is the joint outcome of the decisions made by each player, we also control for the gender, social preferences, and risk preferences of both the buyer and the seller.

Table 2 Probit regressions: the treatment effect on cooperation

Baseline

Restricted threat

Restricted promise

Message-select

Restricted threat

- 0.011

(0.034)

Restricted promise

0.141***

0.147***

(0.037)

(0.037)

Message-select

0.148***

0.166***

0.029

(0.038)

(0.038)

(0.045)

Free-form

0.232***

0.256***

0.124***

0.081*

(0.039)

(0.038)

(0.046)

(0.046)

The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of cooperation on treatment dummies, controlling for gender, social preference, risk preference, and round fixed effects. Two treatments are included for each regression

***, **, and * indicate significance at the 1 % , 5 % , and 10 % levels, respectively

The overall results provide support for Hypotheses I–III. Specifically, the free-form treatment outperforms the restricted promise and message-select treatments, and the restricted promise and message-select treatments outperform the baseline treatment. However, the restricted threat treatment does not perform significantly better than the baseline treatment and fares worse than the restricted promise treatment.

RESULT 2 : A larger number of buyers choose a high price under the restricted promise, message-select, and free-form treatments than under the baseline treatment. Furthermore, more buyers opt for a high price under the free-form treatment than under the restricted promise and message-select treatments. However, there is no significant difference in the high-price ratio between the restricted promise and message-select treatments. Additionally, the high-price ratio is not significantly different between the restricted threat and baseline treatments.

RESULT 3 : A larger number of sellers choose high quality under the restricted promise, message-select, and free-form treatments than under the baseline treatment. Furthermore, more sellers offer high-quality products under the free-form treatment than under the restricted promise and message-select treatments. However, there is no significant difference in the high-quality ratio between the restricted promise and message-select treatments. Additionally, the high-quality ratio is not significantly different between the restricted threat and baseline treatments.

Fig. 3 Cooperative choices by treatments

Figure 3 presents an overview of the ratios of high-price (left panel) and high-quality (right panel) choices across all treatments. The error bars indicate the standard errors. We observe a consistent trend in both variables: the ratio for the restricted threat treatment is equivalent to that of the baseline treatment, while the ratios for the other three treatments surpass that of the baseline. Additionally, the ratios for the restricted promise and message-select treatments are not significantly different from each other but are significantly lower than the ratio for the free-form treatment.

The statistical support for RESULTS 2 and 3 is summarized in Table 3, where we present pairwise comparisons of the ratios of the high-price and high-quality choices made under each treatment. Each cell documents the marginal effect and clustered standard error from one regression. To accommodate the binary dependent variable, we conduct probit regressions of high price or high quality on the treatment dummies. On the left of the table, the dependent variable is high price, which takes a value of 1 if the buyer chooses to offer a high price and 0 otherwise. On the right of the table, the dependent variable is high quality, which takes a value of 1 if the seller chooses to offer a high-quality product and 0 otherwise. The main independent variable is treatment, with the round fixed effects and the decision-maker's gender, social preference and risk preference controlled.

Table 3 Probit regressions: the treatment effect on high price and high quality

Dependent variable: high price

Dependent variable: high quality

Baseline

Restricted threat

Restricted promise

Message-select

Baseline

Restricted threat

Restricted promise

Message-select

Restricted Threat

0.003

(0.054)

- 0.014

(0.034)

Restricted Promise

0.187***

(0.054)

0.179***

(0.056)

0.143***

(0.038)

0.159***

(0.037)

Message-select

0.188***

(0.053)

0.185***

(0.055)

0.006

(0.061)

0.161***

(0.039)

0.178***

(0.037)

0.029

(0.046)

Free-form

0.299***

0.298***

0.129**

0.113*

0.245***

0.270***

0.136***

0.098**

(0.047)

(0.048)

(0.057)

(0.060)

(0.039)

(0.037)

(0.046)

(0.047)

The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of high price and high quality on the treatment dummies, controlling for gender, social preference, risk preference, and round fixed effects. Two treatments are included for each regression

***, **, and * indicate significance at the 1 % , 5 % , and 10 % levels, respectively

5.2 Restricted communication

In Sect. 5.1, Fig. 2 illustrates that the ratio of cooperation achieved under the restricted promise treatment (31.71%) is twice as high as that achieved under the restricted threat treatment (15.43%). However, it is unclear whether this disparity is attributable to a reluctance to use threats or to a lower impact of a threat message under this treatment than under a promise message treatment. In this section, we investigate the distinctions between these two types of treatments to shed light on this matter.

RESULT 4 : In the restricted threat treatment, sellers send a significantly higher number of blank messages compared to the restricted promise treatment. The effectiveness of these blank messages in promoting cooperative behavior is similar across both treatments.

To ensure that promises or threats are not made involuntarily, our game always provides sellers with the option to remain silent by sending a blank message under any of the communication treatments. As shown in Fig. 4, the ratio of blank messages sent is significantly lower under the restricted promise treatment (9.14%) than under the restricted threat treatment (26.86%).Footnote 5 The error bars indicate the standard errors.

Fig. 4 Blank messages in communication treatments

Data from Table 4 shows that when blank messages are sent, the ratios of high-price choices are 12.5% under the restricted promise treatment and 18.09% under the restricted threat treatment. The ratios of high-quality choices are 9.38% and 6.38% for these treatments, respectively. Given the relatively small sample size of blank messages, Mann–Whitney U tests were employed for these comparisons. We found no significant differences in both high-price and high-quality choices between the two treatments (P=0.47 and P=0.57, respectively). Consequently, the effectiveness of blank messages in fostering cooperative behavior is similar across both treatments (P=0.98), with cooperation rates remaining low at approximately 6% in each treatment.

RESULT 5 When the use of blank messages is excluded, the restricted promise treatment remains more effective than the restricted threat treatment in generating cooperation.

As indicated in Table 4, when a promise is made under the restricted promise treatment, the ratios of high-price and high-quality choices are 53.77 % and 34.39 % , respectively. These ratios are significantly higher than the corresponding ratios ( 35.55 % and 19.14 % , respectively) when a threat is made under the restricted threat treatment. Therefore, the cooperation rate resulting from a promise made under the restricted promise treatment is twice that resulting from a threat made under the restricted threat treatment. The finding that making a threat is much less effective than making a promise helps to explain why a majority of players choose not to threaten their counterparts by sending a blank message.

Table 4 The effectiveness of restricted communication

Baseline

Restricted threat

Restricted threat

Restricted promise

Restricted promise

(Message)

(Blank)

(Message)

(Blank)

High price

106/350

91/256

17/94

171/318

4/32

(30.29 % )

(35.55 % )

(18.09 % )

(53.77 % )

(12.50 % )

High quality

61/350

49/256

6/94

110/318

3/32

(17.43 % )

(19.14 % )

(6.38 % )

(34.59 % )

(9.38 % )

Cooperation

58/350

48/256

6/94

109/318

2/32

(16.57 % )

(18.75 % )

(6.38 % )

(34.28 % )

(6.25 % )

The table presents the ratios and percentages (in parentheses) of high price, high quality, and cooperation

RESULT 5 is further supported by the statistical analysis presented in Table 5, which includes comparisons of the restricted promise and restricted threat treatments. Similar to the previous regressions, each cell in the table documents the marginal effect and clustered standard error at the individual level from one regression, with the round fixed effects controlled. In regressions involving the high-price variable, we also control for the buyer's gender, social preference, and risk preference. For regressions involving the high-quality variable, we control for the seller's gender, social preference, and risk preference. In regressions involving cooperation, the characteristics of both the buyer and the seller are controlled. In all three regressions, the promise variable is found to be significant at the 1% level.

Table 5 Probit regressions: the treatment effect of restricted communication after excluding blank messages

High price

High quality

Cooperation

Restricted promise

0.166***

0.156***

0.139***

(0.063)

(0.044)

(0.044)

Only data obtained under the restricted promise and restricted threat treatments with non-blank messages are included. The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of high price, high quality, and cooperation on the treatment dummies, controlling for gender, social preference, risk preference, and round fixed effects. Two treatments are included for each regression

***, **, and * indicate significance at the 1 % , 5 % , and 10 % levels, respectively

5.3 Free-form communication

5.3.1 Classification

To comprehend the contents of the messages, we adopt a coordination game to classify the messages gathered under the free-form communication treatment, similar to the approach used by Houser and Xiao (Reference Houser and Xiao2011). The message evaluators are provided with the instructions given under the free-form communication treatment and tasked with making binary choices (Yes/No) regarding each dimension outlined in Table 6.

Table 6 Classification categories

Categories

Answer

1.Is this message a promise?

Yes

No

2.Is this message a threat?

Yes

No

3.Does this message incorporate the concept of honesty?

Yes

No

4.Does this message incorporate humor?

Yes

No

The evaluation task in our study encompassed four dimensions: promise, threat, honesty, and humor. The impacts of promises and threats on cooperative behavior have been extensively explored in economic literature (Charness & Dufwenberg, Reference Charness and Dufwenberg2006, Reference Charness and Dufwenberg2010; Cooper & Kühn, Reference Cooper and Kai-Uwe2014; Ellingsen & Johannesson, Reference Ellingsen and Johannesson2004; He et al., Reference He, Offerman and Van De Ven2017). These concepts are integral to understanding how commitments and deterrents influence decision-making processes in various economic contexts. In addition, we draw from social psychology to incorporate the notions of honesty and humor into our analysis (Brambilla et al., Reference Brambilla, Rusconi, Sacchi and Cherubini2011; Goodwin et al., Reference Goodwin, Piazza and Rozin2014). Social psychology research underscores how moral and sociability traits influence perceptions and evaluations of others. Notably, warmth, encompassing both morality and sociability, plays a crucial role in how we gather information about others, with morality being a particularly vital factor in human cooperation. In the context of our game, honesty serves as an indicator of morality, while humor signals sociability. These two aspects are essential for understanding how communication influences social dynamics.

The evaluators are aware that these categories are not mutually exclusive. They were compensated according to the consistency of their evaluations regarding the dimensions of three randomly selected messages with the most common evaluations in the session. On average, the evaluators received a payoff of 76.68 RMB, which included a 5 RMB show-up fee. A total of 96 evaluators were recruited for this task, and each evaluator was assigned to categorize half of the messages to control the time and ensure the evaluation quality. To address potential order effects, the messages were presented in reverse order in half of the sessions. Each evaluation session lasted approximately 50 min.

5.3.2 Contents of free-form messages

To provide a sense of how the free-form messages are classified, we start with presenting a selection of sample messages and their corresponding classifications in Table 7.

Figure 5 summarizes the results of message classifications, with error bars indicating the standard errors. Here, we observe the wide use of notions of promise (77.50%) and honesty (56.11%) in the messages. However, only approximately one fifth of the messages use humor (22.22%), and threats are rarely used (7.50%).

Table 7 Examples of messages and their classifications

Message

Promise Notion

Threat Notion

Honesty Notion

Humor Notion

“I’m a five-star seller on Taobao. Let's earn 100 points together!”

Yes (77.08%)

No (97.92%)

No (56.25%)

Yes (91.67%)

“You can quote any price you like.”

No (91.67%)

No (81.25%)

No (93.75%)

No (72.92%)

“As you are in a disadvantaged position, you can only choose to take a risk by trusting me.”

No (95.83 % )

Yes (60.42 % )

No (77.08 % )

No (83.33 % )

“I believe that honesty is essential in trading. The quality of the product I choose will depend on the price you raise.”

Yes (89.58 % )

No (77.08 % )

Yes (100 % )

No (93.75 % )

The classification of each notion (Yes/No) follows the simple majority rule. The ratios in parentheses represent the proportions of evaluators who made the most common evaluation for each notion

Fig. 5 Classification of free-form messages

RESULT 6 Promises and honesty are the most commonly incorporated notions in free-form messages, with humor being present in approximately one fifth of the messages; threats are rarely used.

Next, we explore the effectiveness of each notion included in the contents of free-form messages, namely promise, threat, honesty, and humor.

Table 8 Probit regressions: the effect of notions in free-form messages

Dependent variable

High price

High quality

Cooperation

Promise Notion

0.151***

0.159**

0.203***

(0.059)

(0.075)

(0.073)

Threat Notion

- 0.056

0.039

0.021

(0.096)

(0.093)

(0.082)

Honesty Notion

0.056

0.127**

0.128**

(0.057)

(0.064)

(0.061)

Humor Notion

- 0.019

- 0.100

- 0.076

(0.061)

(0.068)

(0.068)

Observations

360

360

360

Pseudo R 2

0.052

0.101

0.119

The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of high price, high quality, and cooperation on content classification dummies, controlling for gender, social preference, risk preference, and round fixed effects

***, **, and * indicate significance at the 1 % , 5 % , and 10 % levels, respectively

We conduct probit regressions of high price, high quality, and cooperation on the classification dummies, controlling for the round fixed effects and the decision-maker's gender, risk preference, and social preference. As depicted in Table 8, the inclusion of promise and honesty notions in free-form messages significantly enhances cooperation, while the inclusion of threat and humor notions does not yield significant effects. Moreover, a promise notion positively influences both high-price and high-quality choices, whereas an honesty notion affects high-quality choices but not high-price choices.Footnote 6 This result is in line with the social psychology literature (Brambilla et al., Reference Brambilla, Rusconi, Sacchi and Cherubini2011; Goodwin et al., Reference Goodwin, Piazza and Rozin2014). Honesty, as a cue for moral traits, is more closely related to seller's trustworthiness.

RESULT 7a The inclusion of a promise notion increases the ratios of high-price and high-quality choices, thereby promoting cooperation.

RESULT 7b The inclusion of an honesty notion significantly promotes high-quality choices and cooperation.

RESULT 7c The inclusion of a threat or humor notion has no impact on the outcome.

Table 9 Message classification and outcomes

Classification

Message (%)

Cooperation

Contribution to overall cooperation ( % )

Promise only

56 (15.56 % )

25

15.24

Threat only

3 (0.83 % )

0

0.0

Honesty only

2 (0.56 % )

1

0.61

Humor only

19 (5.28 % )

4

2.44

Promise + threat

15 (4.17 % )

7

4.27

Promise + honesty

148 (41.11 % )

85

51.83

Promise + humor

16 (4.44 % )

7

4.27

Threat + honesty

7 (1.94 % )

4

2.44

Honesty + humor

2 (0.56 % )

0

0.0

Promise + threat + honesty

1 (0.28 % )

1

0.61

Promise + threat + humor

1 (0.28 % )

0

0.0

Promise + honesty + humor

42 (11.67 % )

20

12.20

None

42 (11.67 % )

9

5.49

Empty

6 (1.67 % )

1

0.61

Total number of messages

360 (100%)

164

Combinations lacking corresponding messages are omitted from the table

Although we find that promise and honesty notions most effectively promote cooperation, many free-form messages contain more than one notion. To clarify this observation, Table 9 lists the interactions of classifications and their contributions to overall cooperation. In general, cooperative outcomes mostly stem from messages containing only promises, those combining promises and humor, and those combining promises, honesty, and humor. Given that threat and honesty notions rarely appear separately from other notions, RESULTS 7b and 7c are restricted to cases in which the effects come from additional threat and humor notions.

While the human evaluators provide us understanding and measurement from the human perspective, existing dictionaries like LIWC adds a different approach to identify the words used in effective and ineffective free-form messages. In Appendix 1, we provide a brief text analysis by referring to the LIWC 2015 dictionary.

5.3.3 Sincerity of messages and cooperative behavior

To investigate whether the sincerity conveyed in the messages functions as suggested in our theoretical framework, we conducted additional evaluation sessions to assess the sincerity of free-form messages. Evaluators were tasked with rating the sincerity level of messages on a scale from 0 to 10. They were compensated based on the consistency of their sincerity evaluations of six randomly selected messages, compared to other evaluations in the session, using the quadratic scoring rule (see Brier, Reference Brier1950). This was to ensure that the messages were rated earnestly. The average payoff for evaluators was 79.63 RMB, which included a 10 RMB show-up fee. In total, 48 evaluators participated, each tasked to categorize all the free-form messages. To mitigate potential order effects, messages were presented in reverse order in half of the sessions. Each evaluation session lasted approximately 60 min.

RESULT 8: A free-form message with higher sincerity increases the likelihood of high-price and high-quality choices, thereby promoting cooperation.

Table 10 presents the results of probit regressions of high price, high quality, and cooperation on the sincerity rating. We find that messages with higher sincerity ratings significantly encourage the buyer's cooperative behavior (i.e., high price), the seller's cooperative behavior (i.e., high quality), and result in more overall cooperation ( P H , Q H ). This result validates the assumption in our framework that greater sincerity S in messages leads to a higher disutility for the sender if they disappoint others. Consequently, a message's higher sincerity level correlates with more cooperative behavior from both sides due to the increased guilt aversion experienced by the seller and the anticipated increase in guilt aversion from the buyer.

Table 10 Probit regressions: the effect of sincerity in free-form messages

High price

High quality

Cooperation

Sincerity

0.097***

0.109***

0.123***

(0.037)

(0.038)

(0.041)

The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of high price, high quality, and cooperation on the message sincerity, controlling for gender, social preference, risk preference, and round fixed effects

***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively

Upon further regression of sincerity on each of the notion dummies (as shown in Table 11), we observe that sincerity is positively correlated with both the promise and honesty notions (P < 0.01 for both), whereas there is no significant change with the inclusion of either the threat or humor notions.

Table 11 Effect of notions on the sincerity of free-form messages

Dependent variable: sincerity

Promise

Threat

Honesty

Humor

Notion

1.047***

- 0.015

0.697***

0.020

(0.142)

(0.285)

(0.136)

(0.189)

The table presents the effects and the robust standard errors clustered at the individual level (in parentheses) from OLS regressions of the message sincerity on content classification dummies

***, **, and * indicate significance at the 1 % , 5 % , and 10 % levels, respectively

5.4 Message-select vs. free-form communication

The overall comparison of the treatments in Sect. 5.1 indicates a lower level of cooperation under the message-select treatment than under the free-form treatment. This result can be attributed to two possible reasons. First, the sellers under the message-select treatment might not select messages effectively. For instance, they might send a limited number of messages conveying promise and honesty notions, resulting in a reduced willingness of buyers to cooperate. Second, the impact of sending messages containing the same notions might differ between the message-select and free-form treatments.

To understand which of the above two reasons drives the observed difference in the effectiveness of the treatments, we first compare the notions contained in messages under the message-select treatment with those in messages under the free-form treatment. Subsequently, we compare the effects of the same notions in messages under these two treatments.

RESULT 9 The composition of notions is similar between the message-select and free-form communication treatments.

Fig. 6 Comparison of the four notions in messages under the message-select and free-form treatments

Figure 6 demonstrates that the percentages of promise, threat, honesty, and humor notions are very similar between the message-select and free-form treatments. The error bars represent the standard errors. Table 12 presents the results of probit regressions, which confirm the lack of a significant difference in the percentages of messages conveying any of the four notions. Overall, the composition of the notions is comparable between the two treatments. In fact, the use of effective notions (promise and honesty) is slightly more frequent under the message-select treatment than under the free-form treatment, although this difference is not significant. Hence, the difference in effectiveness between the two treatments cannot be attributed to the ineffective use of notions.

Table 12 Probit regressions: use of notions - message-select vs. free-form

Promise notion

Threat notion

Honesty notion

Humor notion

Free-form

- 0.061

- 0.013

- 0.063

- 0.018

(0.041)

(0.029)

(0.051)

(0.045)

Observations

720

720

720

720

Pseudo R 2

0.027

0.028

0.023

0.029

The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of the free-form treatment dummy on content classifications, controlling for gender, social preference, risk preference, and round fixed effects

***, **, and * indicate significance at the 1 % , 5 % , and 10 % levels, respectively

Next, we investigate the second possible reason for the difference in effectiveness between the two treatments: whether the effectiveness of the same notion differs between the message-select treatment and the free-form treatment. The data presented in Table 13 illustrate this phenomenon.

Table 13 The effectiveness of notions

Promise notion (%)

Threat notion (%)

Honesty notion (%)

Humor notion (%)

High price

Message-select

53.69

50.00

54.46

47.56

Free-form

68.10

55.56

68.81

60.00

High quality

Message-select

37.58

37.50

37.05

31.71

Free-form

52.33

48.15

55.45

38.75

Cooperation

Message-select

36.91

37.50

36.61

31.71

Free-form

51.97

44.44

54.95

38.75

The table shows the percentages of high-price choices, high-quality choices, and cooperation associated with messages from the message-select and free-form treatments when the messages contain each of the four classified notions. The notions are not mutually exclusive

When we consider the promise notion, we observe higher ratios of high-price and high-quality choices under the free-form message treatment (68.10% and 52.33%, respectively) than under the message-select treatment (53.69% and 37.58%, respectively). Consequently, the rate of cooperation is also higher under the free-form treatment (51.97%) than under the message-select treatment (36.91%) when the promise notion is included.

Similarly, when we consider the honesty notion, we observe higher ratios of high-price and high quality choices and cooperation under the free-form message treatment (68.81%, 55.45%, and 54.95%, respectively) than under the message-select treatment (54.56%, 37.05%, and 36.61%, respectively).

The rates of cooperation do not differ significantly between the two treatments when threat or humor notions are included.

RESULT 10 . The notions of promise and honesty play a more significant role in fostering cooperation under the free-form treatment than under the message-select treatment.

Statistical support for this finding can be found in Table 14, where we compare the effects of each notion between the message-select and free-form treatments. In the analysis, we include observations associated with each of the four notions in four probit regressions of cooperation on the free-form treatment dummy. Each cell in the table documents the marginal effect and the clustered standard error at the individual level from one regression while controlling for the round fixed effects and the social and risk preferences of the buyer and seller.

Table 14 Probit regression: the effects of notions on cooperation

Dependent variable: cooperation

Promise notion

Threat notion

Honesty notion

Humor notion

Free-form

0.109**

- 0.027

0.126**

- 0.024

(0.051)

(0.122)

(0.054)

(0.079)

Observations

577

51

426

162

Pseudo R 2

0.081

0.295

0.093

0.222

Only data from the message-select and free-form treatments that include each semantic notion are included. The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of cooperation on free-form treatment dummies, controlling for gender, social preference, risk preference, and round fixed effects. ***, **, and * indicate significance at the 1 % , 5 % , and 10 % levels, respectively

The results indicate that messages containing promise or honesty notions are significantly more effective in promoting cooperation under the free-form treatment than under the message-select treatment, at a significance level of 5%. However, no significant differences with respect to the effects of threat and humor notions are observed between these two treatments.

5.5 Dynamics of communication

To understand how sellers’ communication behavior evolves across different communication treatments, we conducted a detailed analysis by treatment. Our analysis begins with the two restricted communication treatments, followed by the comparisons of message-select and free-form treatments treat, in terms of message notions.

RESULT 11 : Sellers increasingly send restricted promises over time in the restricted promise treatment, while there is no discernible trend regarding the use of restricted threats in the restricted threat treatment.

Fig. 7 Dynamics of seller's message choice in restricted communication

Figures 7a, b illustrate the time trends in the proportion of sellers opting for either the restricted threat or restricted promise within their respective treatments. We note a gradual upward trend in the adoption of restricted promises, suggesting a learning curve where sellers increasingly understand the benefits of using such promises. In contrast, the usage pattern of restricted threats displays no consistent trend across different rounds, possibly due to their limited effectiveness within the parameters of our game. Statistical support for this finding can be found in Table 15, where probit regressions were conducted on the binary message choice against round variables, while controlling for the sellers’ gender, risk preference, and social preference. In line with earlier analyses, marginal effects were assessed, and standard errors were clustered at the individual level. The frequency of sellers issuing restricted promises exhibits a marginal yet progressive increase over time (P = 0.052). On the other hand, the employment of restricted threats shows no significant trend (P = 0.715).

Table 15 Probit regressions: the effect of rounds under restricted communication

Restricted threat

Restricted promise

Round

0.003

0.011*

(0.007)

(0.006)

The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of seller's message choice dummies on the round variables, controlling for the seller's gender, social preference and risk preference

***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively

We further explore the dynamics of message choice in the message-select and the free-form treatments by examining the time trends of each notion by treatment, as depicted in Figs. 8a and 8b.

Fig. 8 Dynamics of seller message notions in message-select and free-form

RESULT 12 . In the free-form treatment, sellers gradually increase their use of messages incorporating the notion of honesty or humor, while there is no evident time trend for any notion categories in the message-select treatment.

As documented in Table 16, in the message-select treatment, the use of messages incorporating each notion fluctuates over time, with no evident trend observed in probit regressions of the notion dummy on the round variables (P > 0.1 for all notion categories). Conversely, in the free-form treatment, there is a gradual increase in the use of messages incorporating notions of honesty or humor (P = 0.045 and P = 0.002, respectively), while no significant trends are observed for the promise and threat notions (P > 0.1 for both notion categories).

Table 16 Probit regressions: the effect of rounds under message-select and free-form

Promise notion

Threat notion

Honesty notion

Humor notion

Message-select

Round

- 0.012

0.004

- 0.006

0.010

(0.008)

(0.005)

(0.009)

(0.008)

Free-form

Round

- 0.001

- 0.001

0.020**

0.024***

(0.009)

(0.005)

(0.010)

(0.008)

The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of content classification dummies on the round variables, controlling for the seller's gender, social preference and risk preference. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively

5.6 The treatment effect of sending promises

Finally, we shift our attention to examining whether the effect of sending a promise varies across treatments. Specifically, we compare the treatment effects of sending a promise between the restricted promise, message-select, and free-form treatments. This comparison is intended to clarify whether the differences in treatment outcomes are indeed influenced by how the message is constructed or selected.

Theoretically, we can conduct a similar analysis regarding the treatment effect of sending a threat. However, we refrain from drawing any conclusions in this regard because of the extremely small sample of threat notions sent under the message-select and free-form treatments.

RESULT 13 . Under the free-form treatment, the promise notion significantly promotes cooperation compared with the message-select and restricted promise treatments. However, no significant differences are observed when comparing the restricted promise treatment with the message-select treatment in terms of the impact on cooperation.

The promise notion is prevalent, appearing in more than 77% of the messages sent under any of the restricted promise, message-select, and free-form treatments. When a message containing a promise notion is sent, both sellers and buyers exhibit an increased inclination to cooperate under the free-form treatment, as evidenced by the data in Table 17 and the regressions documented in Table 18. The ratios of high-price and high-quality choices are significantly higher under the free-form treatment than under the restricted promise and message-select treatments.

Table 17 The effectiveness of a promise notion across treatments

Restricted promise

Message-select

Free-form

High price

171/318 ( 53.77 % )

160/298 ( 53.69 % )

190/279 ( 68.10 % )

High quality

110/318 ( 34.59 % )

112/298 ( 37.58 % )

146/279 ( 52.33 % )

Cooperation

109/318 ( 34.28 % )

110/298 ( 36.91 % )

145/279 ( 51.97 % )

Table 18 Probit regressions: behavior conditional on the promise notion

High price

High quality

Cooperation

Restricted promise

Message-select

Restricted promise

Message-select

Restricted promise

Message-select

Message-select

- 0.014

0.031

0.026

(0.064)

(0.049)

(0.046)

Free-form

0.126**

0.129**

0.166***

0.125**

0.153***

0.109**

(0.062)

(0.062)

(0.051)

(0.051)

(0.052)

(0.051)

The table presents the marginal effects and standard errors clustered at the individual level (in parentheses) from probit regressions of high price, high quality, and cooperation on treatment dummies, conditional on the sending of a promise notion during pre-play communication; the regressions control for gender, social preference, risk preference, and round fixed effects. Two treatments are included for each regression. ***, **, and * indicate significance at the 1 % , 5 % , and 10 % levels, respectively

Conversely, there are no discernible differences between the choices of the sellers and buyers under the restricted promise and message-select treatments. Cooperation rates are also similar between these two treatments.

6 Conclusions

This paper investigates the reasons underlying the effectiveness of free-form communication in promoting efficient outcomes. To achieve this, we use a sequential social dilemma game wherein the buyer proposes a price and the seller selects a quality level. We examine five treatments: no communication (i.e., the baseline), a restricted promise, a restricted threat, a message selected from a set of previously constructed free-form messages, and a self-constructed free-form message.

We observe that the cooperation rate under the message-select treatment is equivalent to that under the restricted promise treatment but significantly lower than that under the free-form treatment. Furthermore, our findings demonstrate that the restricted promise treatment significantly enhances cooperation, whereas the restricted threat treatment shows no improvement compared with the baseline treatment.

Following Ellingsen and Johannesson (Reference Ellingsen and Johannesson2004) and Vanberg (Reference Vanberg2008), who introduce the concepts of lying aversion and guilt aversion to explain the superiority of a restricted promise over no communication, we propose a similar rationale to elucidate why free-form communication surpasses a restricted promise in terms of effectiveness. Our hypothesis is based on the assumption that individuals experience a higher level of disutility when sending messages using their own words than when they rely on pre-formulated promises. To capture this phenomenon, we introduce the concept of sincerity, which quantifies the persuasiveness of a statement, leading to the identification of new Pareto-efficient equilibria in free-form communication.

Our work is inspired by the theoretical and empirical efforts of economists and psychologists who have investigated the function and emergence of language (e.g., Blume et al., Reference Blume, DeJong, Kim and Sprinkle1998; Bryan et al., Reference Bryan, Walton, Rogers and Dweck2011; Reference Bryan, Adams and Monin2013; Chou, Reference Chou2015; Cremer et al., Reference Cremer, Garicano and Prat2007; Fillenbaum & Rapoport, Reference Fillenbaum and Rapoport1971; Hong & Zhao, Reference Hong and Zhao2017; Rubinstein, Reference Rubinstein2000; Selten & Warglien, Reference Selten and Warglien2007). Focusing on the meaning of language in the context of a social dilemma, we conducted a content analysis with the assistance of 96 incentivized evaluators to categorize the notions. Our results show that free-form messages predominantly convey promises and honesty, which are also the most effective notions for promoting cooperative behavior. This indicates that our participants have an accurate perception of which notions are most effective in a natural language context. Additionally, while similar notions are present in both message-select and free-form messages, the effectiveness of the same message is reduced when it is selected rather than self-constructed by the sender. This finding confirms that the self-constructed nature of free-form communication is the key factor that makes it more effective than other tested means of communication: although the content of the message matters, its self-constructed nature plays a crucial role in its sincerity and, consequently, its impact.

Furthermore, 48 additional incentivized evaluators were employed to rate the sincerity of the messages. We found that cooperative behavior in both sellers and buyers increases with the sincerity of the messages, and that the sincerity rating is higher with the inclusion of promise and honesty notions. Our dynamic analysis of communication behavior revealed that individuals gradually learn to send more promises in the restricted promise treatment and more honesty and humor notions in free-form messages.

Although free-form communication consistently promotes efficient outcomes, the factors driving its effectiveness might differ across environments. It would be interesting to discuss the possibility of a more universal model that would explain our findings and align with those of other studies. The effectiveness of communication may be related to the role of additional content in reducing social distance as demonstrated in games with cooperation or coordination opportunities (see Coffman & Niehaus, Reference Coffman and Niehaus2020; Dugar & Shahriar, Reference Dugar and Shahriar2018; Mohlin & Johannesson, Reference Mohlin and Johannesson2008; Wang & Houser, Reference Wang and Houser2019). While social distance may not be the primary concern in games with more pronounced conflicts (e.g., Turmunkh et al., Reference Turmunkh, Van den Assem and Van Dolder2019), type signaling may still account for the superior performance of free-form communication over restricted communication. A comparison of games that span the spectrum from pure coordination to zero-sum scenarios would be valuable in terms of comprehending the dominant functions at play in each environment. By systematically examining games with varying degrees of conflict, we can gain a more comprehensive understanding of the factors that contribute to the effectiveness of free-form communication in different game settings. This avenue of research could shed light on the nuanced dynamics of communication and cooperation in diverse scenarios.

This paper provides insights into essential aspects of the mechanisms by which the sincerity of natural language communication impacts the outcomes of sequential social dilemma games. However, further experimental and theoretical research is necessary to study the effects of free-form communication in other social and economic environments and thus deepen our understanding. Exploring the role of natural language communication in diverse contexts will provide valuable insights into the broader implications of such communication for cooperation and general interactive decision-making processes.

Declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix 1. A different approach of text analysis

To explore the content of free-form messages from another angle, we apply text analysis using the LIWC 2015 dictionary. Figure 9 provides a summary of the most commonly used words in these messages,Footnote 7 focusing on those occurring in more than 1% of the total words.

Fig. 9 Summary of word frequencies in free-form messages

We categorized the messages based on their ability to promote cooperation into two groups: effective and ineffective messages. Effective messages led to high price and high quality outcomes, signifying successful cooperation, whereas ineffective messages failed to foster cooperation. Our analysis shows that terms linked with promises, such as“high price,” “high quality,” and “high,” are prominently used in both types of messages. However, these terms are about 20% more frequent in effective messages, underscoring the importance of clear goals in achieving cooperative outcomes. For example, a typical effective message might be: “Please raise a high price, and I will sell you a high-quality product”.

Additionally, effective messages tend to have a slightly higher occurrence of words associated with honesty, like “trust” and “honesty.” Representative messages include phrases like “Honesty is most important” and “Live up to trust”.

Appendix 2. Omitted proofs

Proof of restricted promise communication

Empty-talk equilibrium

Suppose that the seller's signaling strategy is ( S θ H = 0 , S θ L = 0 ). The buyer's best response is to offer P L , allowing both types to earn 50. To ensure that both types have no incentive to deviate, we must specify the buyer's response to S = 1 . If this response is P H , θ H earns 100, which exceeds his payoff from sending S = 0 . Therefore, we must have r 1 [ 0 , 3 4 ) to ensure that the buyer's best response to S = 1 is P L . Then, both types have no reason to deviate, as both earn 50 - ω < 50 .

Thus, there exists a pooling equilibrium where ( S θ H = 0 , S θ L = 0 ) . The buyer's best response is always P L , while the seller's optimal quality decision is as follows: type θ H offers Q H when S = 1 and P = P H , and Q L otherwise, while type θ L offers Q L regardless of the values of S and P. Regarding the buyer's belief, we must set r 0 = p ( θ H ) and r 1 [ 0 , 3 4 ) .

Limited sincerity pooling equilibrium

Suppose that the seller's signaling strategy is ( S θ H = 1 , S θ L = 1 ) . The buyer's best response depends on p ( θ H ) , as r 1 = p ( θ H ) .

If p ( θ H ) [ 0 , 3 4 ) , the buyer's best response is to offer P L so that both θ H and θ L can earn 50 - ω . However, both types can earn 50 if they deviate to S = 0 . Therefore, this equilibrium does not exist if p ( θ H ) [ 0 , 3 4 ) .

If p ( θ H ) 3 4 , 1 , the buyer's best response is to offer P H so that θ H and θ L can earn 100 and 200 - θ L - ω , respectively. To ensure that both types have no incentive to deviate, we need to specify the buyer's response to S = 0 . As the buyer's best response is always P L , allowing both types to earn only 50, there is no incentive to deviate.

Thus, if p ( θ H ) 3 4 , 1 , there exists a pooling equilibrium where ( S θ H = 1 , S θ L = 1 ) . The buyer's best response is P H , given S = 1 , and P L otherwise. The seller's optimal quality decision is as follows: type θ H offers Q H when S = 1 and P = P H , and Q L otherwise, while type θ L offers Q L regardless of S and P. Regarding the buyer's belief, we must set r 1 = p ( θ H ) but place no restriction on r 0 .

We omit the discussion of other equilibria, as they do not exist.

Proof of message-select communication

Empty-talk equilibrium

Suppose that the seller's signaling strategy is ( S θ H = 0 , S θ L = 0 ) . The buyer's best response is to offer P L , allowing both types to earn 50. To ensure that neither type has an incentive to deviate, we must specify the buyer's response to N S > 0 . If the buyer's response to any N S > 0 is P H , then θ H earns 100, which exceeds his payoff from sending S = 0 . Accordingly, we must set r α [ 0 , 3 4 ) for α in N α > 0 to ensure that the buyer's best response to S = α is P L . Then, neither type has a reason to deviate, as both types earn 50 - ω < 50 .

Thus, there exists a pooling equilibrium where ( S θ H = 0 , S θ L = 0 ) . The buyer's best response is always P L , while the seller's optimal quality decision is as follows: type θ H offers Q H when N S > 0 and P = P H , and Q L otherwise, while type θ L offers Q L regardless of S and P. Regarding the buyer's belief, we must set r 0 = p ( θ H ) and r α [ 0 , 3 4 ) for α in N α > 0 .

Limited sincerity pooling equilibria

Suppose that the seller's signaling strategy is ( S θ H = α , S θ L = α ) , where N α > 0 . The buyer's best response depends on p ( θ H ) , as r α = p ( θ H ) .

If p ( θ H ) [ 0 , 3 4 ) , the buyer's best response is to offer P L so that both θ H and θ L can earn 50 - ω . However, both types can earn 50 if they deviate to S = 0 . Therefore, this type of equilibrium does not exist if p ( θ H ) [ 0 , 3 4 ) .

If p ( θ H ) 3 4 , 1 , the buyer's best response is to offer P H so that θ H and θ L can earn 100 and 200 - α · θ L - ω , respectively. To ensure that neither type has an incentive to deviate, we must specify the buyer's response to other messages. When S = 0 , the buyer's best response is always P L so that both θ H and θ L can only earn 50. Neither type has an incentive to deviate. The buyer's best response to sincerity other than S = α and S = 0 depends on his off-equilibrium belief. Here, we need not restrict the off-equilibrium belief for any N S > α because neither type can earn more through deviation, regardless of the buyer's best response. However, we must restrict the off-equilibrium belief for α > S > 0 such that the buyer's best response is always P L , given these messages. Therefore, we must set r S [ 0 , 3 4 ) for S in α > S > 0 .

Thus, if p ( θ H ) 3 4 , 1 , there exist pooling equilibria where ( S θ H = α , S θ L = α ) , N α > 0 . The buyer's best response is always P H , given S = α , or P L , given α > S 0 . Her price decision depends on r S when N S > α . The seller's optimal quality decision is as follows: type θ H offers Q H when N S > 0 and P = P H , and Q L otherwise, while type θ L offers Q L regardless of S and P. Regarding the buyer's belief, we must set r α = p ( θ H ) and r S [ 0 , 3 4 ) for S in α > S > 0 but place no restriction on other off-equilibrium beliefs.

We omit the discussion of other equilibria, as they do not exist.

Proof of free-form communication

Limited sincerity pooling equilibria

Suppose that the seller's signaling strategy is ( S θ H = α , S θ L = α ) , where k - 1 α > 0 . The buyer's best response depends on p ( θ H ) , as r α = p ( θ H ) .

If p ( θ H ) [ 0 , 3 4 ) , the buyer's best response is to offer P L so that both θ H and θ L can earn 50 - ω . However, the buyer's best response to N S k is always P H , and both types can earn 100. Thus, there is incentive to deviate, and this type of equilibrium does not exist.

If p ( θ H ) 3 4 , 1 , the buyer's best response is to offer P H so that θ H and θ L can earn 100 and 200 - α · θ L - ω , respectively. To ensure that neither type has an incentive to deviate, we must specify the buyer's response to other messages. When S = 0 , the buyer's best response is always P L so that both θ H and θ L can only earn 50. Neither type has an incentive to deviate. Similarly, when N S k , the buyer's best response is always P H so that both types can earn 100; again, there is no incentive to deviate. The buyer's best response to sincerity other than S = α , S = 0 , and N S k depends on his off-equilibrium belief. Here, we need not restrict the off-equilibrium belief for any k - 1 S > α because neither type can earn more through deviation, regardless of the buyer's best response. However, we must restrict the off-equilibrium belief for α > S > 0 such that the buyer's best response is always P L , given these messages. Therefore, we must set r S [ 0 , 3 4 ) for S in α > S > 0 .

Thus, if p ( θ H ) 3 4 , 1 , there exist pooling equilibria where ( S θ H = α , S θ L = α ) , k - 1 α > 0 . The buyer's best response is always P H , given N S k or S = α , or P L , given α > S 0 . Her price decision depends on r S when k - 1 S > α . The seller's optimal quality decision is as follows: type θ H offers Q H given N S > 0 and P H , and Q L otherwise, while type θ L offers Q H given N S k and P H , and Q L otherwise. Regarding the buyer's belief, we must set r α = p ( θ H ) and r S [ 0 , 3 4 ) for S in α > S > 0 but place no restriction on other off-equilibrium beliefs.

High sincerity pooling equilibria

Suppose that both θ H and θ L pool on a sufficiently sincere statement, where N S θ H = S θ L = α k . The buyer's best response to α is to offer P H , allowing both types to earn 100. To ensure that neither type has an incentive to deviate, we must specify the buyer's response to other messages. When S = 0 , the buyer's best response is always P L so that both θ H and θ L can only earn 50. Neither type has an incentive to deviate. When k - 1 S > 0 , the buyer's best response must always be P L to ensure that type θ L has no incentive to deviate. Thus, we must set r S [ 0 , 3 4 ) for k - 1 S > 0 . When S [ k , α ) ( α , N ] , the buyer's best response is always P H . Both types can earn 100 and have no incentive to deviate.

Thus, there exist pooling equilibria where ( S θ H = α , S θ L = α ) , N α k . The buyer's best response is P H , given N S k , and P L otherwise. The seller's optimal quality decision is as follows: type θ H offers Q H given N S > 0 and P H , and Q L otherwise, while type θ L offers Q H given N S k and P H , and Q L otherwise. Regarding the buyer's belief, we must set r α = p ( θ H ) and r S [ 0 , 3 4 ) for S in k - 1 S > 0 but place no restriction on other off-equilibrium beliefs.

High sincerity separating equilibria

Suppose that θ H and θ L separate on sufficiently sincere statements, where N S θ H = α k , N S θ L = β k and α β . The buyer has an updated belief, namely r α = 1 , r β = 0 , and her best responses corresponding to these beliefs are P H and P H , respectively. Accordingly, both types can earn 100. To ensure that neither type has an incentive to deviate, we must specify the buyer's responses to other messages. When S = 0 , the buyer's best response is always P L so that both θ H and θ L can only earn 50. Neither type has an incentive to deviate. When k - 1 S > 0 , the buyer's best response must always be P L to ensure that seller type θ L has no incentive to deviate. Therefore, we must set r S [ 0 , 3 4 ) for k - 1 S > 0 . If seller type θ L chooses S = α , the buyer's best response is P H so that type θ L can earn 100 and has no incentive to deviate. Likewise, if seller type θ H chooses S = β , the buyer's best response is P H so that type θ L can earn 100 and has no incentive to deviate. The buyer's best response to sincerity other than S = α , S = β , and k - 1 S 0 remains to be determined. In this case, the buyer's best response is always P H , regardless of the off-equilibrium beliefs, allowing both types to earn 100 and removing their incentive to deviate.

Thus, there are separating equilibria where ( S θ H = α , S θ L = β ) , with N α k , N β k , and α β . The buyer's best response is P H , given N S k , and P L otherwise. The seller's optimal quality decision is as follows: type θ H offers Q H , given N S > 0 and P H , and Q L otherwise, while type θ L offers Q H , given N S k and P H , and Q L otherwise. Regarding the buyer's belief, we must set r α = 1 , r β = 0 and r S [ 0 , 3 4 ) for k - 1 S > 0 but place no restriction on other off-equilibrium beliefs.

We omit the discussion of other equilibria, as they do not exist.

Appendix 3. Instructions

Instructions for the baseline treatment

Welcome to the Smith Experimental Economics Research Center at Shanghai Jiao Tong University. You are going to participate in an economics experiment on decision-making. You can be paid during the experiment. Your earnings will depend on the choices that you and other participants make during the experiment, as well as some random factors. At the end of the experiment, each participant will be paid privately.

During the experiment, it is important that you do not talk with the other participants, and you will need to follow our given instructions. If you have any questions, please raise your hand; our experimenter will come to you to answer your questions.

We promise that the information collected during the experiment will be kept strictly confidential, and the data will only be used for academic research.

The experimental procedure

You will play a 10-round game with the same rules. At the beginning of each round, you will be randomly paired with another participant in this room. In each round, one member of the pair will be randomly selected as the seller, while the other will be selected as the buyer.

The buyer first decides which price to choose. If a high price is chosen, the buyer must pay 200 tokens to the seller; if a low price is chosen, the buyer must pay 50 tokens. The seller can observe the buyer's choice and then determine the quality of the product. For a high-quality product, the cost of production is 100 tokens, and the buyer will earn 300 tokens; for a low-quality product, the cost of production is 0, and the buyer will earn 100 tokens.

Rules of Profit Calculation:

Buyer's revenue = Value of the product - Buyer's bid

Seller's revenue = Buyer's bid - Cost of production

In other words, if the buyer chooses a high price and the seller chooses high quality, both will obtain 100 tokens. If the buyer chooses a high price and the seller chooses low quality, the buyer will lose 100 tokens and the seller will obtain 200 tokens. If the buyer chooses a low price and the seller chooses high quality, the buyer will obtain 250 tokens and the seller will lose 50 tokens. If the buyer chooses a low price and the seller chooses low quality, both will obtain 50 tokens.

When the decisions are settled, we will provide feedback on the results to each participant at the end of each round. This feedback will include your assigned role (buyer/seller), the price and quality decisions, and the revenue obtained by you and your paired participant. During the game, your private trading history will be available at the bottom left corner of the screen, which will include all of your feedback given in previous rounds.

Payoff calculation

We will randomly draw one round to calculate your payoff. For every 5 tokens you obtain, you will receive 1 RMB.

When the 10-round game ends, you will need to complete a follow-up questionnaire, which will collect your personal information. You will also earn some tokens when you complete the questionnaire. If you complete both parts successfully, you will receive a 15 RMB show-up fee and an extra 20 RMB for the 10-round game to cover your potential losses.

When the experiment is over, please wait patiently in your seat. The experimenter will distribute the earnings separately to each participant based on your identification number.

Merged instructions for treatments with communication

For all treatments with communication

Welcome to the Smith Experimental Economics Research Center at Shanghai Jiao Tong University. You are going to participate in an economics experiment on decision-making. You can be paid during the experiment. Your earnings will depend on the choices that you and other participants make during the experiment, as well as some random factors. At the end of the experiment, each participant will be paid privately.

During the experiment, it is important that you do not talk with the other participants, and you will need to follow our given instructions. If you have any questions, please raise your hand; our experimenter will come to you to answer your questions.

We promise that the information collected during the experiment will be kept strictly confidential, and the data will only be used for academic research.

The procedure of the experiment

You are going to play a 10-round game with the same rules. At the beginning of each round, you will be randomly paired with another participant in this room. In each round, one member of the pair will be randomly selected as the seller, while the other will be selected as the buyer. The paired participants will make a transaction.

Restricted threat treatment only

Before the transactional decisions are made in each round, the seller can send a message to the buyer. In this stage, the seller can choose between the following two options:

  1. 1. “If you pay a low price, I’ll choose low quality.”

  2. 2. “ ” (An empty message)

Restricted promise treatment only

Before the transactional decisions are made in each round, the seller can send a message to the buyer. In this stage, the seller can choose between the following two options:

  1. 1. “If you pay a high price, I’ll choose high quality.”

  2. 2. “ ” (An empty message)

Message-select treatment only

Before the transactional decisions are made in each round, the seller can send a message to the buyer. In each round, the seller can choose between 10 options and an empty message. In each round, the options are randomly drawn (without replacement) from a corpus collected during previous experiments. The contents of the previous experiments and the origin of the corpus will be reviewed in a subsequent section of these instructions.

Free-form treatment only

Before the transactional decisions are made in each round, the seller can send a message to the buyer through a text box. An empty message is allowed. Please do not include any personal information in the message.

For all treatments with communication

The buyer will receive the seller's message and decide which price to choose. If a high price is chosen, the buyer must pay 200 tokens to the seller; if a low price is chosen, the buyer must pay 50 tokens. The seller can observe the buyer's choice and then determine the quality of the product. For a high-quality product, the cost of production is 100 tokens and the buyer will earn 300 tokens; for a low-quality product, the cost of production is zero and the buyer will earn 100 tokens.

Rules of Profit Calculation:

Buyer's revenue = Value of the product - Buyer s bid
Seller's revenue = Buyer's bid - Cost of production

In other words, if the buyer chooses a high price and the seller chooses high quality, both will obtain 100 tokens. If the buyer chooses a high price and the seller chooses low quality, the buyer will lose 100 tokens and the seller will obtain 200 tokens. If the buyer chooses a low price and the seller chooses high quality, the buyer will obtain 250 tokens and the seller will lose 50 tokens. If the buyer chooses a low price and the seller chooses low quality, both will obtain 50 tokens.

When the decisions are settled, we will provide feedback on the results to each participant at the end of each round. This feedback will include your assigned role (buyer/seller),the price and quality decisions, and the revenue obtained by you and your paired participant. During the game, your private trading history will be available at the bottom left and bottom right corner of the screen, which will include all of your feedback given in previous rounds, as well as the messages sent/received.

Payoff calculation

We will randomly draw one round to calculate your payoff. For every 5 tokens you obtain, you will receive 1 RMB.

When the 10-round game ends, you will need to complete a follow-up questionnaire, which will collect your personal information. You will also earn some tokens when you complete the questionnaire. If you complete both parts successfully, you will receive a 15 RMB show-up fee and an extra 20 RMB for the 10-round game to cover your potential losses.

When the experiment is over, please wait patiently in your seat. The experimenter will distribute the earnings separately to each participant.

Message-select treatments only

The Origin of the Corpus

As mentioned above, the options provided to sellers during the message transmission stage were collected during a previous experiment. Actually, the designs of the current and previous experiments are almost identical; the only difference lies in the message transmission stage. In the previous experiment, the seller could write a message to the buyer through a text box (empty messages were allowed), and the only restriction on the message was that no personal information should be revealed.

We integrated all of the messages sent in the previous experiment and obtained a corpus of 355 sentences (after excluding five empty messages). In each round, the options available to the seller will be randomly drawn from this corpus by the computer. Some of the messages may be similar or even identical, as some participants follow a consistent strategy when sending messages in multiple rounds.

Instructions for message classification

Welcome to the Smith Experimental Economics Research Center at Shanghai Jiao Tong University. You are going to participate in an economics experiment on decision-making. You can be paid during the experiment. Your earnings will depend on the choices that you and the other participants make during the experiment. At the end of the experiment, each participant will be paid privately.

During the experiment, it is important that you do not talk with the other participants, and you will need to follow our given instructions. If you have any questions, please raise your hand; our experimenter will come to you to answer your questions.

We promise that the information collected in the experiment will be kept strictly confidential, and the data will only be used for academic research.

The procedure of the experiment

In this experiment, you will be required to code some messages. These messages were all generated during a previous experiment. Before classifying each message, please read these instructions carefully. The details and a description of the previous experiment are provided below. This information will help you better understand the role these messages played in the previous experiment.

Experimental procedure of the previous experiment

In the previous experiment, the participants were required to play a 10-round game with the same rules. At the beginning of each round, each participant was randomly paired with another. In each round, one member of each pair was randomly selected as the seller, while the other was selected as the buyer.

The paired participants were required to make a transaction. Before the transactional decisions were made in each round, the seller could send a message to the buyer through a chat box. An empty message was allowed. The seller was not allowed to identify himself/herself in the message.

The buyer received a message from the seller and then decided which price to choose. If a high price was chosen, the buyer needed to pay 200 tokens to the seller; if a low price was chosen, the buyer needed to pay 50 tokens. The seller could observe the buyer's choice and then determine the quality of the product. For a high-quality product, the cost of production was 100 tokens, and the buyer earned 300 tokens; for a low-quality product, the cost of production was 0, and the buyer earned 100 tokens.

Rules of Profit Calculation:

Buyer`s \,revenue = Value\, of\, the\, product - Buyer`s\, bid
Seller`s\, revenue = Buyer`s \,bid - Cost\, of\, production

In other words, if the buyer chose a high price and the seller chose high quality, both would obtain 100 tokens. If the buyer chose a high price and the seller chose low quality, the buyer would lose 100 tokens and the seller would obtain 200 tokens. If the buyer chose a low price and the seller chose high quality, the buyer would obtain 250 tokens and the seller would lose 50 tokens. If the buyer chose a low price and the seller chose low quality, both would obtain 50 tokens.

When the decisions were settled, feedback on the results was provided to each participant at the end of each round. This feedback included the assigned role (buyer/seller), the price and quality decisions, and the revenue obtained by the seller and buyer in the group. Only one round was randomly drawn to calculate the participants’ payoffs. For every 5 tokens, the participant received 1 RMB.

Rules of this message classification experiment

In this experiment, the messages you will classify were generated by sellers during the above-mentioned experiment.

For each message, you will need to make a binary choice (Y/N) in the following four dimensions:

  1. 1. Is this message a promise?

  2. 2. Is this message a threat?

  3. 3. Does this message include the concept of honesty?

  4. 4. Does this message include humor?

Payoff calculation

When the experiment is over, we will randomly select three messages to calculate your final payoff. Your profit will depend on whether your classifications are consistent with the most popular evaluation.

For each dimension, we will follow the principle of a simple majority: if your choice is consistent with that of more than 50 % of the participants, you will receive a reward of 7 RMB for that dimension; otherwise, you will receive no reward. If there is a tie, the computer will randomly select one of the options (Y/N) to calculate the final payoff.

Besides the payoff for message categorization, you will receive a 5 RMB show-up fee if you successfully complete the experiment. When the classification ends, you will need to complete a follow-up questionnaire, which will collect your personal information.

After the experiment is over, please wait patiently in your seat. The experimenter will distribute the earnings separately to each participant.

Instructions for sincerity evaluation

Welcome to the Smith Experimental Economics Research Center at Shanghai Jiao Tong University. You are going to participate in an economics experiment on decision-making. You can be paid during the experiment. Your earnings will depend on the choices that you and the other participants make during the experiment. At the end of the experiment, each participant will be paid privately.

During the experiment, it is important that you do not talk with the other participants, and you will need to follow our given instructions. If you have any questions, please raise your hand; our experimenter will come to you to answer your questions.

We promise that the information collected in the experiment will be kept strictly confidential, and the data will only be used for academic research.

The procedure of the experiment

In this experiment, you will be required to rate some messages. These messages were all generated during a previous experiment. Before rating each message, please read these instructions carefully. The details and a description of the previous experiment are provided below. This information will help you better understand the role these messages played in the previous experiment.

Experimental procedure of the previous experiment

In the previous experiment, the participants were required to play a 10-round game with the same rules. At the beginning of each round, each participant was randomly paired with another. In each round, one member of each pair was randomly selected as the seller, while the other was selected as the buyer.

The paired participants were required to make a transaction. Before the transactional decisions were made in each round, the seller could send a message to the buyer through a chat box. An empty message was allowed. The seller was not allowed to identify himself/herself in the message.

The buyer received a message from the seller and then decided which price to choose. If a high price was chosen, the buyer needed to pay 200 tokens to the seller; if a low price was chosen, the buyer needed to pay 50 tokens. The seller could observe the buyer's choice and then determine the quality of the product. For a high-quality product, the cost of production was 100 tokens, and the buyer earned 300 tokens; for a low-quality product, the cost of production was 0, and the buyer earned 100 tokens.

Rules of Profit Calculation:

Buyer`s \,revenue = Value\, of\, the\, product - Buyer`s\, bid
Seller ` s revenue = Buyer`s \,bid - Cost\, of\, production

In other words, if the buyer chose a high price and the seller chose high quality, both would obtain 100 tokens. If the buyer chose a high price and the seller chose low quality, the buyer would lose 100 tokens and the seller would obtain 200 tokens. If the buyer chose a low price and the seller chose high quality, the buyer would obtain 250 tokens and the seller would lose 50 tokens. If the buyer chose a low price and the seller chose low quality, both would obtain 50 tokens.

When the decisions were settled, feedback on the results was provided to each participant at the end of each round. This feedback included the assigned role (buyer/seller), the price and quality decisions, and the revenue obtained by the seller and buyer in the group. Only one round was randomly drawn to calculate the participants’ payoffs. For every 5 tokens, the participant received 1 RMB.

Task in this experiment

In this experiment, the messages you will rate were generated by sellers during the above-mentioned experiment. For each message, you will need to evaluate its “sincerity” on a scale from 0 to 10.

Payoff calculation

When the experiment is over, we will randomly select six messages to calculate your final payoff. Your earning for each message (counted in RMB) is calculated as follows:

12 - 0.1 × ( Your rating - Mean rating of all participants ) 2

In other words, for each message, the closer your rating is to the mean rating given by all participants in this experiment, the higher your earnings will be. This is designed to encourage careful rating of each message.

Besides the payoff from the rating task, you will receive a 10 RMB show-up fee if you successfully complete the experiment. When the rating task ends, you will need to complete a follow-up questionnaire, which will collect your personal information.

After the experiment is over, please wait patiently in your seat. The experimenter will distribute the earnings separately to each participant.

Appendix 4. Demographics in each treatment

See Table 19.

Table 19 Demographics in each treatment

Baseline

Restricted threat

Restricted promise

Message-select

Free-form

Gender

0.61

0.61

0.56

0.67

0.57

(0.49)

(0.49)

(0.50)

(0.47)

(0.50)

Risk

43.46

46.16

46.34

45.00

47.21

(18.30)

(16.00)

(16.72)

(15.77)

(16.43)

Social

11.53

10.21

14.04

12.88

16.29

(10.30)

(11.65)

(11.22)

(12.57)

(13.10)

N

70

70

70

72

72

Each column presents the mean values of demographics and preferences in the corresponding the treatment, with standard deviations noted in parentheses for clarity. The risk preference is measured using the bomb risk elicitation task, as described by Crosetto and Filippin (Reference Crosetto and Filippin2013). For measuring social preference, we employ the dictator game, wherein each participant decides the amount to distribute from a total of 50 experimental currency units

Footnotes

This research received funding support from the Shanghai Jiao Tong University Smith Experimental Economics Research Center and the National Natural Science Foundation of China (Grant No. 72371090). We extend our gratitude to the guest editors and two anonymous referees for their insightful feedback. We are also thankful for the valuable comments from Jun Feng, Lata Gangadharan, Philip Grossman, Xi Zhi Lim, Delong Meng, Erte Xiao, and attendees at seminars at George Mason University, McMaster University, Monash University, University of Guelph, Wichita State University. Additionally, we appreciate the feedback received at the ESA World Meeting (Lyon), the 16th Australian and New Zealand Experimental Economics Workshop, the ESA Global Online Around-the-Clock Meetings, and the China Behavioral and Experimental Economics Forum (Shanghai). The replication material for the study is available at https://doi.org/https://doi.org/10.17605/OSF.IO/YR927.

1 Page 4, lines 16–18.

2 The message-select treatment was implemented in November 2020 to allow time to organize and program all of the messages as options into the z-Tree program (Fischbacher, Reference Fischbacher2007).

3 The table 19 in the appendix offers comprehensive details on demographic variables, risk, and social preferences.

4 The buyer's price decision on the off-equilibrium path depends on her updated belief.

5 Z = 4.79, P < 0.001 for probit regressions of blank messages on treatment dummies, controlling for gender, social preference, risk preference, and round fixed effect; clustered standard errors are corrected at the individual level.

6 It is noteworthy that each notion is represented by a binary dummy in our analysis. Messages encompassing more than one notion may have multiple dummies set to one.

7 Pronouns and conjunctions are omitted from this analysis.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Figure 0

Fig. 1 The sequential social dilemma game

Figure 1

Table 1 Summary of the treatments

Figure 2

Fig. 2 Distribution of outcomes

Figure 3

Table 2 Probit regressions: the treatment effect on cooperation

Figure 4

Fig. 3 Cooperative choices by treatments

Figure 5

Table 3 Probit regressions: the treatment effect on high price and high quality

Figure 6

Fig. 4 Blank messages in communication treatments

Figure 7

Table 4 The effectiveness of restricted communication

Figure 8

Table 5 Probit regressions: the treatment effect of restricted communication after excluding blank messages

Figure 9

Table 6 Classification categories

Figure 10

Table 7 Examples of messages and their classifications

Figure 11

Fig. 5 Classification of free-form messages

Figure 12

Table 8 Probit regressions: the effect of notions in free-form messages

Figure 13

Table 9 Message classification and outcomes

Figure 14

Table 10 Probit regressions: the effect of sincerity in free-form messages

Figure 15

Table 11 Effect of notions on the sincerity of free-form messages

Figure 16

Fig. 6 Comparison of the four notions in messages under the message-select and free-form treatments

Figure 17

Table 12 Probit regressions: use of notions - message-select vs. free-form

Figure 18

Table 13 The effectiveness of notions

Figure 19

Table 14 Probit regression: the effects of notions on cooperation

Figure 20

Fig. 7 Dynamics of seller's message choice in restricted communication

Figure 21

Table 15 Probit regressions: the effect of rounds under restricted communication

Figure 22

Fig. 8 Dynamics of seller message notions in message-select and free-form

Figure 23

Table 16 Probit regressions: the effect of rounds under message-select and free-form

Figure 24

Table 17 The effectiveness of a promise notion across treatments

Figure 25

Table 18 Probit regressions: behavior conditional on the promise notion

Figure 26

Fig. 9 Summary of word frequencies in free-form messages

Figure 27

Table 19 Demographics in each treatment