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Bounded rationality and correlated equilibria

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Abstract

We study an interactive framework that explicitly allows for non-rational behavior. We do not place any restrictions on how players can deviate from rational behavior. Instead we assume that there exists a lower bound p E [0,1] such that all players play and are believed to play rationally with a probability p or more. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary p E [0,1]. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information, and they can be applied to observed frequencies of play to compute a measure p that bounds from below the probability with which any given player is choosing actions consistent with payoff maximization and common knowledge of payoff maximization.

Suggested Citation

  • Fabrizio Germano & Peio Zuazo-Garin, 2015. "Bounded rationality and correlated equilibria," Economics Working Papers 1468, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:1468
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    1. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    2. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    3. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    4. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    5. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
    6. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications, Elsevier.
    7. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    8. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    9. Hu, Tai-Wei, 2007. "On p-rationalizability and approximate common certainty of rationality," Journal of Economic Theory, Elsevier, vol. 136(1), pages 379-391, September.
    10. Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters,in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287 World Scientific Publishing Co. Pte. Ltd..
    11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    12. Dirk Bergemann & Stephen Morris, 2013. "The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency," Levine's Working Paper Archive 786969000000000730, David K. Levine.
    13. Fabrizio Germano & Peio Zuazo-Garin, 2015. "Uncertain rationality and robustness in games with incomplete information," Economics Working Papers 1470, Department of Economics and Business, Universitat Pompeu Fabra.
    14. Ignacio Palacios-Huerta & Oscar Volij, 2008. "Experientia Docet: Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 76(1), pages 71-115, January.
    15. John Conlisk, 1996. "Why Bounded Rationality?," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 669-700, June.
    16. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    17. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    18. Graham Mallard, 2012. "Modelling Cognitively Bounded Rationality: An Evaluative Taxonomy," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 674-704, September.
    19. R. M. Harstad & R. Selten., 2014. "Bounded-Rationality Models: Tasks to Become Intellectually Competitive," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.
    20. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    21. Robert J. Aumann & Jacques H. Dreze, 2008. "Rational Expectations in Games," American Economic Review, American Economic Association, vol. 98(1), pages 72-86, March.
    22. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    23. Fabrizio Germano & Jonathan Weinstein & Peio Zuazo-Garin, 2016. "Uncertain Rationality, Depth of Reasoning and Robustness in Games with Incomplete Information," Economics Working Papers 1548, Department of Economics and Business, Universitat Pompeu Fabra.
    24. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    25. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    26. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    27. Sergiu Hart & Yishay Mansour, 2013. "How Long To Equilibrium? The Communication Complexity Of Uncoupled Equilibrium Procedures," World Scientific Book Chapters,in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 10, pages 215-249 World Scientific Publishing Co. Pte. Ltd..
    28. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
    29. Terri Kneeland, 2015. "Identifying Higher‐Order Rationality," Econometrica, Econometric Society, vol. 83(5), pages 2065-2079, September.
    30. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2010. "Signaling and mediation in games with common interests," Games and Economic Behavior, Elsevier, vol. 68(2), pages 670-682, March.
    31. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 395-415.
    32. V. P. Crawford., 2014. "Boundedly Rational versus Optimization-Based Models of Strategic Thinking and Learning in Games," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.
    33. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," CORE Discussion Papers 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    34. P.-A. Chiappori, 2002. "Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer," American Economic Review, American Economic Association, vol. 92(4), pages 1138-1151, September.
    35. repec:dau:papers:123456789/157 is not listed on IDEAS
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    Keywords

    strategic interaction; correlated equilibrium; robustness to bounded rationality; approximate knowledge; incomplete information; measure of rationality; experiments.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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