Beliefs and (In)Stability in Normal-Form Games

Hyndman, Kyle and Terracol, Antoine and Vaksmann, Jonathan (2013): Beliefs and (In)Stability in Normal-Form Games.

Abstract

In this paper, we use experimental data to study players' stability in normal-form games where subjects have to report beliefs and to 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 30% 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 70% apply different levels of reasoning to different games.

• Item Type: MPRA Paper
• Language: English
• Keywords: Game theory, Beliefs, Stability, Level-$k$ thinking
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C91 - Laboratory, Individual Behavior; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness

References

Agranov, Marina, Elizabeth Potamites, Andrew Schotter, Chloe Tergiman. 2012. Beliefs and endogenous cognitive levels: An experimental study. Games and Economic Behavior 75(2) 449–463.

Camerer, Colin, Teck-Hua Ho, Juin-Kuan Chong. 2004. A cognitive hierarchy model of games. Quarterly Journal of Economics 119(3) 861–898.

Costa-Gomes, Miguel A., Vincent P. Crawford. 2006. Cognition and behavior in two-person guessing games: An experimental study. American Economic Review 96(5) 1737–1768.

Costa-Gomes, Miguel A., Vincent P. Crawford, Bruno Broseta. 2001. Cognition and behavior in normal-form games: An experimental study. Econometrica 69(5) 1193–1235.

Costa-Gomes, Miguel A., Vincent P. Crawford, Nagore Iriberri. 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.

Costa-Gomes, Miguel A., Georg Weizs ̈acker. 2008. Stated beliefs and play in normal-form games. Review of Economic Studies 75(3) 729–762.

Crawford, Vincent P., Miguel A. Costa-Gomes, Nagore Iriberri. 2013. Structural models of nonequilibrium strategic thinking: Theory, evidence, and applications. Journal of Economic Literature 51(1) 5–62.

Danz, David, Dietmar Fehr, Dorothea Ku ̈bler. 2012. Information and beliefs in a repeated normal-form game. Experimental Economics 15(4) 622–640.

Georganas, Sotiris, Paul J. Healy, Roberto A. Weber. 2010. On the persistence of strategic sophistication.

Goeree, Jacob K., Charles A. Holt. 2004. A model of noisy introspection. Games and Economic Behavior 46(2) 365–382.

Haruvy, Ernan. 2002. Identification and testing of modes in beliefs. Journal of Mathematical Psychology 46(1) 88–109.

Manski, Charles F. 2002. Identification of decision rules in experiments on simple games of proposal and response. European Economic Review 46(4-5) 880–891.

Manski, Charles F. 2004. Measuring expectations. Econometrica 72(5) 1329–1376.

McKelvey, Richard D., Thomas R. Palfrey. 1995. Quantal response equilibria for normal form games. Games and Economic Behavior 10(1) 6–38.

Nagel, Rosemarie. 1995. Unraveling in guessing games: An experimental study. American Economic Review 85(5) 1313–26.

Stahl, Dale O., Paul W. Wilson. 1994. Experimental evidence on players’ models of other players. Journal of Economic Behavior & Organization 25(3) 309–327.

Stahl, Dale O., Paul W. Wilson. 1995. On players’ models of other players: Theory and experimental evidence. Games and Economic Behavior 10(1) 218–254.

Trautmann, S.T., G. van de Kuilen. 2011. Belief elicitation: A horse race among truth serums. Discussion Paper 2011-117, Tilburg University, Center for Economic Research.