Hostname: page-component-7b9c58cd5d-hpxsc Total loading time: 0 Render date: 2025-03-15T09:04:50.143Z Has data issue: false hasContentIssue false
  • English
  • Français

Eliciting beliefs in continuous-choice games: a double auction experiment

Published online by Cambridge University Press:  14 March 2025

Claudia Neri
Claudia Neri*
Affiliation:
Department of Economics, University of St. Gallen, Varnbüelstrasse 19, 9000 St. Gallen, Switzerland
*
[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a methodology to implement probabilistic belief elicitation in continuous-choice games. Representing subjective probabilistic beliefs about a continuous variable as a continuous subjective probability distribution, the methodology involves eliciting partial information about the subjective distribution and fitting a parametric distribution on the elicited data. As an illustration, the methodology is applied to a double auction experiment, where traders’ beliefs about the bidding choices of other market participants are elicited. Elicited subjective beliefs are found to differ from proxies such as Bayesian Nash equilibrium beliefs and empirical beliefs, both in terms of the forecasts of other traders’ bidding choices and in terms of the best-response bidding choices prescribed by beliefs. Elicited subjective beliefs help explain observed bidding choices better than BNE beliefs and empirical beliefs. By extending probabilistic belief elicitation beyond discrete-choice games to continuous-choice games, the proposed methodology enables to investigate the role of beliefs in a wider range of applications.

Keywords

Probabilistic beliefsBelief elicitationPrivate informationExperiments
Type
Original Paper
Information
Experimental Economics , Volume 18 , Issue 4 , December 2015 , pp. 569 - 608
Copyright
Copyright © 2015 Economic Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Electronic supplementary material The online version of this article (doi:https://doi.org/10.1007/s10683-014-9420-1) contains supplementary material, which is available to authorized users.

References

Armantier, O, & Treich, N (2009). Subjective probabilities in games: An application to the overbidding puzzle. International Economic Review, 50(4), 1079–1102 2590002 10.1111/j.1468-2354.2009.00560.xCrossRefGoogle Scholar
Armantier, O, & Treich, N (2013). Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging. European Economic Review, 62, 17–40. 10.1016/j.euroecorev.2013.03.008CrossRefGoogle Scholar
Bellemare, C., Sebald, A., & Strobel, M. (2010). Measuring the willingness to pay to avoid guilt: Estimation using equilibrium and stated belief models. Journal of Applied Econometrics. https://ideas.repec.org/p/iza/izadps/dp4803.html.Google Scholar
Bellemare, C, Sebald, A, & Strobel, M (2011). Measuring the willingness to pay to avoid guilt: Estimation using equilibrium and stated belief models. Journal of Applied Econometrics, 26, 437–453 2767790 10.1002/jae.1227CrossRefGoogle Scholar
Bellemare, C., Bissonnette, L., & Kröger, S. (2012). Flexible approximation of subjective expectations using probability questions. Journal of Business and Economic Statistics, 30(1), 213–245.CrossRefGoogle Scholar
Blanco, M, Engelmann, D, Normann, H, & Koch, A (2010). Belief elicitation in experiments: Is there a hedging problem?. Experimental Economics, 13(4), 412–438 1198.91054 10.1007/s10683-010-9249-1CrossRefGoogle Scholar
Camerer, C., Ho, T., Chong, J., & Weigelt, K. (2002). Strategic teaching and equilibrium models of repeated trust and entry games. Mimeo: CalTech.Google Scholar
Camerer, C., & Hua Ho, T. (1999). Experience-weighted attraction learning in normal form games. Econometrica, 67(4), 827–874.CrossRefGoogle Scholar
Cason, T, & Friedman, D (1997). Price formation in single call markets. Econometrica, 65(2), 311–345 0872.90015 10.2307/2171895CrossRefGoogle Scholar
Cheung, YW, & Friedman, D (1997). Individual learning in normal form games: Some laboratory results. Games and Economic Behavior, 19(1), 46–76 0876.90105 1448507 10.1006/game.1997.0544CrossRefGoogle Scholar
Costa-Gomes, M, & Weizsäcker, G (2008). Stated beliefs and play in normal-form games. Review of Economic Studies, 75(3), 729–762 1141.91351 2433112 10.1111/j.1467-937X.2008.00498.xCrossRefGoogle Scholar
Danz, DN, Fehr, D, & Kübler, D (2012). Information and beliefs in a repeated normal-form game. Experimental Economics, 15(4), 622–640. 10.1007/s10683-012-9317-9CrossRefGoogle Scholar
Engelberg, J, Manski, C, & Williams, J (2009). Comparing the point predictions and subjective probability distributions of professional forecasters. Journal of Business and Economic Statistics, 27(1), 30–41 2484982 10.1198/jbes.2009.0003CrossRefGoogle Scholar
Erev, I., & Roth, A. (1998). Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. The American Economic Review, 88(4), 848–881.Google Scholar
Fudenberg, D, & Levine, D (1998). Learning in games. European Economic Review, 42(3), 631–639. 10.1016/S0014-2921(98)00011-7CrossRefGoogle Scholar
Haruvy, E, Lahav, Y, & Noussair, C (2007). Traders’ expectations in asset markets: Experimental evidence. The American Economic Review, 97(5), 1901–1920. 10.1257/aer.97.5.1901CrossRefGoogle Scholar
Hoffrage, U., Lindsey, S., Hertwig, R., & Gigerenzer, G. (2000). Communicating statistical information. Science, 290(5500), 2261–2262.CrossRefGoogle ScholarPubMed
Hommes, C, Sonnemans, J, Tuinstra, J, & Velden, HVD (2005). Coordination of expectations in asset pricing experiments. Review of Financial Studies, 18(3), 955 10.1093/rfs/hhi003CrossRefGoogle Scholar
Hyndman, K, Özbay, E, Schotter, A, & Ehrblatt, WZ (2012). Convergence: An experimental study of teaching and learning in repeated games. Journal of the European Economic Association, 10(3), 573–604. 10.1111/j.1542-4774.2011.01063.xCrossRefGoogle Scholar
Kirchkamp, O, & Reiß, JP (2011). Out-of-equilibrium bids in first-price auctions: Wrong expectations or wrong bids. The Economic Journal, 121(557), 1361–1397. 10.1111/j.1468-0297.2011.02455.xCrossRefGoogle Scholar
Manski, C (2002). Identification of decision rules in experiments on simple games of proposal and response. European Economic Review, 46(4–5), 880–891. 10.1016/S0014-2921(01)00222-7CrossRefGoogle Scholar
Manski, C (2004). Measuring expectations. Econometrica, 72(5), 1329–1376 1137.91361 10.1111/j.1468-0262.2004.00537.xCrossRefGoogle Scholar
Manski, C, & Neri, C (2013). First-and second-order subjective expectations in strategic decision-making: Experimental evidence. Games and Economic Behavior, 81(C), 232–254 1282.91076 3095931 10.1016/j.geb.2013.06.001CrossRefGoogle Scholar
Nyarko, Y, & Schotter, A (2002). An experimental study of belief learning using elicited beliefs. Econometrica, 70(3), 971–1005 1121.91317 1910409 10.1111/1468-0262.00316CrossRefGoogle Scholar
Palfrey, T, & Wang, S (2009). On eliciting beliefs in strategic games. Journal of Economic Behavior & Organization, 71(2), 98–109. 10.1016/j.jebo.2009.03.025CrossRefGoogle Scholar
Rey-Biel, P (2009). Equilibrium play and best response to (stated) beliefs in normal form games. Games and Economic Behavior, 65(2), 572–585 1156.91331 2501715 10.1016/j.geb.2008.03.003CrossRefGoogle Scholar
Rustichini, A, Satterthwaite, M, & Williams, S (1994). Convergence to efficiency in a simple market with incomplete information. Econometrica, 62(5), 1041–1063 0820.90031 10.2307/2951506CrossRefGoogle Scholar
Rutström, E, & Wilcox, N (2009). Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test. Games and Economic Behavior, 67(2), 616–632 1190.91040 2574124 10.1016/j.geb.2009.04.001CrossRefGoogle Scholar
Seidenfeld, T (1985). Calibration, coherence, and scoring rules. Philosophy of Science, 52, 274–294 804568 10.1086/289244CrossRefGoogle Scholar
Smith, V, Suchanek, G, & Williams, A (1988). Bubbles, crashes, and endogenous expectations in experimental spot asset markets. Econometrica, 56(5), 1119–1151. 10.2307/1911361CrossRefGoogle Scholar
Sonnemans, J, Hommes, C, Tuinstra, J, & Velden, HVD (2004). The instability of a heterogeneous cobweb economy: A strategy experiment on expectation formation. Journal of Economic Behavior & Organization, 54(4), 453–481. 10.1016/j.jebo.2003.02.004CrossRefGoogle Scholar
Supplementary material: File

Neri supplementary material

Experimental Procedures
Download Neri supplementary material(File)
File 109.2 KB