Hostname: page-component-7b9c58cd5d-g9frx Total loading time: 0 Render date: 2025-03-15T09:04:48.480Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimating depth of reasoning in a repeated guessing game with no feedback

Published online by Cambridge University Press:  14 March 2025

Mariano Runco
Mariano Runco*
Affiliation:
Department of Economics, Auburn University at Montgomery, 7071 Senators Drive, 36117 Montgomery, AL, USA
*
e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper estimates depth of reasoning in an Iterative Best Response model using data from Weber (2003) ten-period repeated guessing game with no feedback. Different mixture models are estimated and the type (Level-0, Level-1, etc) of each player is determined in every round using the Expectation Maximization algorithm. The matrices showing the number of individuals transitioning among levels is computed in each case. It is found that most players either remain in the same level or advance to the next two levels they were in the previous period. The lowest levels (Level-0 and Level-1) have a higher probability of transitioning to a higher level than Level-2 or Level-3. Thus, we can conclude that subjects, through repetition of the task, quickly become more sophisticated strategic thinkers as defined by higher levels. However, in some specifications the highest levels have a relatively large probability of switching to a lower level in the next period. In general, depth of reasoning increases monotonically in small steps as individuals are subjected to the same task repeatedly.

Keywords

GamesBeauty-contest experimentLearningFinite mixture modelEM algorithmTransition matrix

JEL classification

D72: Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior D83: Search • Learning • Information and Knowledge • Communication • Belief • Unawareness C50: General
Type
Original Paper
Information
Experimental Economics , Volume 16 , Issue 3 , September 2013 , pp. 402 - 413
Copyright
Copyright © 2012 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.)

References

Bosch-Domenech, A., Montalvo, J., Nagel, R., & Satorra, A. (2002). One, two, (three), infinity, …: newspaper and lab beauty-contest experiments. American Economic Review, 92(5), 1687–1701. 10.1257/000282802762024737CrossRefGoogle Scholar
Bosch-Domenech, A., Montalvo, J., Nagel, R., & Satorra, A. (2010). A finite mixture analysis of beauty contest data using generalized beta distribution. Experimental Economics, 13(4), 461–475. 10.1007/s10683-010-9251-7CrossRefGoogle Scholar
Breitmoser, Y. (2012). Strategic reasoning in p-beauty contest. Games and Economic Behavior, 75(2), 555–569. 10.1016/j.geb.2012.02.010CrossRefGoogle Scholar
Camerer, C. (2003). Behavioral game theory: experiments in strategic interaction, Princeton: Princeton University Press.Google Scholar
Camerer, C., & Ho, T. (1999). Experience-weighted attraction learning in normal form games. Econometrica, 67(4), 827–874. 10.1111/1468-0262.00054CrossRefGoogle Scholar
Cheung, Y., & Friedman, D. (1997). Individual learning in normal form games: some laboratory results. Games and Economic Behavior, 19, 46–76. 10.1006/game.1997.0544CrossRefGoogle Scholar
Costa-Gomes, M., & Crawford, V. (2006). Cognition and behavior in two-person guessing games: an experimental study. American Economic Review, 96(5), 1737–1768. 10.1257/aer.96.5.1737CrossRefGoogle Scholar
Costa-Gomes, M., Crawford, V., & Broseta, B. (2001). Cognition and behavior in normal-form games: an experimental study. Econometrica, 69(5), 1193–1235. 10.1111/1468-0262.00239CrossRefGoogle Scholar
Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society B, 39, 1–38.CrossRefGoogle Scholar
Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans, Philadelphia: SIAM 10.1137/1.9781611970319CrossRefGoogle Scholar
Erev, I., & Roth, A. (1998). Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria. American Economic Review, 88(4), 848–881.Google Scholar
Goeree, J., & Holt, C. (2004). A model of noisy introspection. Games and Economic Behavior, 46, 365–382. 10.1016/S0899-8256(03)00145-3CrossRefGoogle Scholar
McKelvey, R., & Palfrey, T. (1999). Quantal response equilibria for normal form games. Games and Economic Behavior, 10, 6–35. 10.1006/game.1995.1023CrossRefGoogle Scholar
McLachlan, G., & Peel, D. (2000). Finite mixture models, New York: Wiley 10.1002/0471721182CrossRefGoogle Scholar
Nagel, R. (1995). Unraveling in guessing games: an experimental study. American Economic Review, 85(5), 1313–1326.Google Scholar
Nagel, R., Bosch-Domenech, A., & Satorra, A. Montalvo, J. (1999). One, two, (three), infinity: newspaper and lab beauty-contest experiments. Economics and business working paper series, paper #438, Universitat Pompeu Fabra, Barcelona.Google Scholar
Stahl, D. (1996). Boundedly rational rule learning in a guessing game. Games and Economic Behavior, 16, 303–330. 10.1006/game.1996.0088CrossRefGoogle Scholar
Stahl, D. (2000). Rule learning in symmetric normal form games: theory and evidence. Games and Economic Behavior, 32, 105–138. 10.1006/game.1999.0754CrossRefGoogle Scholar
Stahl, D., & Wilson, P. (1995). On players’ models of other players: theory and experimental evidence. Games and Economic Behavior, 10, 213–254. 10.1006/game.1995.1031CrossRefGoogle Scholar
Weber, R. (2003). Learning with no feedback in a competitive guessing game. Games and Economic Behavior, 44, 134–144. 10.1016/S0899-8256(03)00002-2CrossRefGoogle Scholar