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Behavior and Learning in the “Dirty Faces” Game

Published online by Cambridge University Press:  14 March 2025

Roberto A. Weber
Roberto A. Weber*
Affiliation:
Department of Social and Decision Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA
*
email: [email protected]
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Abstract

This paper examines the Dirty Faces problem as a Bayesian game. The equilibrium in the general form of the game requires the extreme assumption of common knowledge of rationality. However, for any finite number of players, the exact number of steps of iterated rationality necessary for the equilibrium to arise depends on the number of players of a particular type, allowing the game to be used to bound the number of steps satisfied by actual players. The game differs from other games used to study iterated rationality in that all players are better off when common knowledge of rationality is satisfied. While behavior in experiments is inconsistent with the game-theoretic prediction at the group level, individual level behavior shows a greater degree of consistency with theory and with previous results on iterated rationality. Finally, there is some evidence of learning in repeated play.

Keywords

game theorycommon knowledge

JEL classification

C91: Laboratory, Individual Behavior C92: Laboratory, Group Behavior C72: Noncooperative Games
Type
Research Article
Information
Experimental Economics , Volume 4 , Issue 3 , December 2001 , pp. 229 - 242
Copyright
Copyright © 2002 Economic Science Association

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References

Aumann, R.J. (1995). “Backward Induction and Common Knowledge of Rationality.” Games and Economic Behavior. 8, 6–19.CrossRefGoogle Scholar
Bernheim, D. (1984). “Rationalizable Strategic Behavior.” Econometrica. 52, 1007–1028.CrossRefGoogle Scholar
Binmore, K. and Brandenburger, A. (1990). “Common Knowledge and Game Theory.” In Binmore, K. (ed.), Essays on the Foundations of Game Theory. Basil Blackwell, Oxford.Google Scholar
Camerer, C.F., Johnson, E., Rymon, T., and Sen, S. (1993). “Cognitions and Framing in Sequential Bargaining for Gains and Losses.” In Binmore, K., Kirman, A., and Tani, P. (eds.), Frontiers of Game Theory. MIT Press, Cambridge.Google Scholar
Costa-Gomes, M., Crawford, V., and Broseta, B. (2000). “Cognition and Behavior in Normal-Form Games: An Experimental Study.” Unpublished Manuscript.Google Scholar
Fudenberg, D. and Tirole, J. (1993). Game Theory. MIT Press, Cambridge.Google Scholar
Geanakoplos, J. (1994). “Common Knowledge.” In Aumann, R.J. and Hart, S. (eds.), Handbook of Game Theory. Vol. 2. Elsevier, Amsterdam.Google Scholar
Ho, T.H., Weigelt, K., and Camerer, C. (1998). “Iterated Dominance and Iterated Best-Response in Experimental ‘p-Beauty Contest’ Games.” The American Economic Review. 88, 947–969.Google Scholar
Kahneman, D. and Tversky, A. (1979). “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica. 47, 263–291.CrossRefGoogle Scholar
Kahneman, D. and Tversky, A. (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty.” Journal of Risk and Uncertainty. 5, 297–323.Google Scholar
Littlewood, J.E. (1953). A Mathematician's Miscellany. London, England: Meuthen & Co. Ltd.Google Scholar
McKelvey, R.D. and Page, T. (1990). “Public and Private Information: An Experimental Study of Information Pooling.” Econometrica. 58, 1321–1339.CrossRefGoogle Scholar
McKelvey, R.D. and Palfrey, T.R. (1992). “An Experimental Study of the Centipede Game.” Econometrica. 60, 803–836.CrossRefGoogle Scholar
Nagel, R. (1995). “Experimental Results on Interactive Competitive Guessing.” The American Economic Review. 85, 1313–1326.Google Scholar
Pearce, D. (1984). “Rationalizable Strategic Behavior and the Problem of Perfection.” Econometrica. 52, 10291050.CrossRefGoogle Scholar
Rapoport, A. and Amaldoss, W. (2000). “Mixed Strategies and Iterative Elimination of Strongly Dominated Strategies: An Experimental Investigation of States of Knowledge.” Journal of Economic Behavior and Organization. 42, 483–521.CrossRefGoogle Scholar
Rubinstein, A. (1989). “The Electronic Mail Game: Strategic Behavior Under ‘Almost Common Knowledge’.” The American Economic Review. 79, 385–391.Google Scholar
Stahl, D.O. II and Wilson, P.W. (1994). Experimental Evidence on Players’ Models of Other Players.” Journal of Economic Behavior and Organization. 25, 309–327.CrossRefGoogle Scholar
Stahl, D.O. II and Wilson, P.W. (1995). “On Players’ Models of Other Players: A New Theory and Experimental Evidence.” Games and Economic Behavior. 10, 218–254.CrossRefGoogle Scholar