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Beliefs and (in)stability in normal-form games

Published online by Cambridge University Press:  14 March 2025

Kyle Hyndman Open the ORCID record for Kyle Hyndman [Opens in a new window] ,
Antoine Terracol  and
Jonathan Vaksmann
Kyle Hyndman*
Affiliation:
University of Texas at Dallas, Richardson, USA
Antoine Terracol*
Affiliation:
LED, Université Paris 8 Vincennes - Saint-Denis, Saint-Denis, France
Jonathan Vaksmann*
Affiliation:
GAINS-TEPP, IRA, Le Mans Université, Le Mans, France
*
kyleb.hyndman@utdallas.edu, url: https://hyndman-honhon.com/kyle-hyndman.html
antoine.terracol@univ-paris8.fr
jonathan.vaksmann@univ-lemans.fr
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Abstract

In this paper, we use experimental data to study players’ stability in normal-form games where subjects have to report beliefs and choose actions. Subjects saw each of 12 games four times in a regular or isomorphic form spread over two days without feedback. We document a high degree of stability within the same (strategically equivalent) game, although time and changes in the presentation of the game do lead to less stability. To look at stability across different games, we adopt the level-k theory, and show that stability of both beliefs and actions is significantly lower. Finally, we estimate a structural model in which players either apply a consistent level of reasoning across strategically different games, or reasoning levels change from game to game. Our results show that approximately 23% of subjects apply a consistent level of reasoning across the 12 games, but that they assign a low level of sophistication to their opponent. The remaining 77% apply different levels of reasoning to different games. We show that this may be due to subjects being attracted to the action with the highest possible payoff.

Keywords

Game theoryBeliefsStabilityLevel-k thinkingExperimentC72C91D83
Type
Original Paper
Information
Experimental Economics , Volume 25 , Issue 4 , September 2022 , pp. 1146 - 1172
Copyright
Copyright © The Author(s), under exclusive licence to Economic Science Association 2022

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s10683-022-09747-w.

References

Agranov, M., Potamites, E., Schotter, A., & Tergiman, C. (2012). Beliefs and endogenous cognitive levels: An experimental study. Games and Economic Behavior, 75(2), 449–463. 10.1016/j.geb.2012.02.002CrossRefGoogle Scholar
Avoyan, A., & Schotter, A. (2020). Attention in games: An experimental study. European Economic Review 124 Article 103410.CrossRefGoogle Scholar
Camerer, C., Ho, T-H, & Chong, J-K (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics, 119(3), 861–898. 10.1162/0033553041502225CrossRefGoogle Scholar
Costa-Gomes, M. A., & Crawford, V. P. (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. A., Crawford, V. P., & Broseta, B. (2001). Cognition and behavior in normal-form games: An experimental study. Econometrica, 69(5), 1193–1235. 10.1111/1468-0262.00239CrossRefGoogle Scholar
Costa-Gomes, M. A., Crawford, V. P., & Iriberri, N. (2009). Comparing models of strategic thinking in van huyck, battalio, and beil’s coordination games. Journal of the European Economic Association, 7(2–3), 365–376. 10.1162/JEEA.2009.7.2-3.365CrossRefGoogle Scholar
Costa-Gomes, M. A., & Weizsäcker, G. (2008). Stated beliefs and play in normal-form games. Review of Economic Studies, 75(3), 729–762. 10.1111/j.1467-937X.2008.00498.xCrossRefGoogle Scholar
Crawford, V. P., Costa-Gomes, M. A., & Iriberri, N. (2013). Structural models of nonequilibrium strategic thinking: Theory, evidence, and applications. Journal of Economic Literature, 51(1), 5–62. 10.1257/jel.51.1.5CrossRefGoogle Scholar
Danz, D., 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
Georganas, S., Healy, P. J., & Weber, R. A. (2015). On the persistence of strategic sophistication. Journal of Economic Theory, 159(A), 369–400. 10.1016/j.jet.2015.07.012CrossRefGoogle Scholar
Goeree, J. K., & Holt, C. A. (2004). A model of noisy introspection. Games and Economic Behavior, 46(2), 365–382. 10.1016/S0899-8256(03)00145-3CrossRefGoogle Scholar
Haruvy, E. (2002). Identification and testing of modes in beliefs. Journal of Mathematical Psychology, 46(1), 88–109. 10.1006/jmps.2001.1378CrossRefGoogle Scholar
Manski, C. F. (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. F. (2004). Measuring expectations. Econometrica, 72(5), 1329–1376. 10.1111/j.1468-0262.2004.00537.xCrossRefGoogle Scholar
McKelvey, R. D., & Palfrey, T. R. (1995). Quantal response equilibria for normal form games. Games and Economic Behavior, 10(1), 6–38. 10.1006/game.1995.1023CrossRefGoogle Scholar
Nagel, R. (1995). Unraveling in guessing games: An experimental study. American Economic Review, 85(5), 1313–26.Google Scholar
Stahl, D. O., & Wilson, P. W. (1994). Experimental evidence on players’ models of other players. Journal of Economic Behavior & Organization, 25(3), 309–327. 10.1016/0167-2681(94)90103-1CrossRefGoogle Scholar
Stahl, D. O., & Wilson, P. W. (1995). On players’ models of other players: Theory and experimental evidence. Games and Economic Behavior, 10(1), 218–254. 10.1006/game.1995.1031CrossRefGoogle Scholar
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