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Bayesian Game Theorists and non-Bayesian Players

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  • Guilhem Lecouteux

    (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UniCA - Université Côte d'Azur)

Abstract

Bayesian game theorists claim to represent players as Bayes rational agents, maximising their expected utility given their beliefs about the choices of other players. I argue that this narrative is inconsistent with the formal structure of Bayesian game theory. This is because (i) the assumption of common belief in rationality is equivalent to equilibrium play, as in classical game theory, and (ii) the players' prior beliefs are a mere mathematical artefact and not actual beliefs held by the players. Bayesian game theory is thus a Bayesian representation of the choice of players who are committed to play equilibrium strategy profiles.
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  • Guilhem Lecouteux, 2018. "Bayesian Game Theorists and non-Bayesian Players," Working Papers halshs-01633126, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01633126
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01633126v2
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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Lauren Larrouy & Guilhem Lecouteux, 2017. "Mindreading and endogenous beliefs in games," Journal of Economic Methodology, Taylor & Francis Journals, vol. 24(3), pages 318-343, July.
    3. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    4. Jean-Pierre Ponssard, 1975. "A note on the L-P formulation of zero sum sequential games with incomplete information," Post-Print hal-00364274, HAL.
    5. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    6. PONSSARD, Jean-Pierre & ZAMIR, Shmuel, 1973. "Zero-sum sequential games with incomplete information," LIDAM Reprints CORE 149, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    8. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    9. Nicola Giocoli, 2003. "Modeling Rational Agents," Books, Edward Elgar Publishing, number 2585.
    10. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396.
    11. Robert J. Aumann & Jacques H. Dreze, 2008. "Rational Expectations in Games," American Economic Review, American Economic Association, vol. 98(1), pages 72-86, March.
    12. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    13. Milgrom, Paul, 1981. "An Axiomatic Characterization of Common Knowledge," Econometrica, Econometric Society, vol. 49(1), pages 219-222, January.
    14. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    15. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    16. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    17. Gerardo Infante & Guilhem Lecouteux & Robert Sugden, 2016. "Preference purification and the inner rational agent: a critique of the conventional wisdom of behavioural welfare economics," Journal of Economic Methodology, Taylor & Francis Journals, vol. 23(1), pages 1-25, March.
    18. R. J. Aumann & J. H. Dreze, 2009. "Assessing Strategic Risk," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 1-16, February.
    19. Cubitt, Robin P. & Sugden, Robert, 2003. "Common Knowledge, Salience And Convention: A Reconstruction Of David Lewis' Game Theory," Economics and Philosophy, Cambridge University Press, vol. 19(2), pages 175-210, October.
    20. John C. Harsanyi, 1962. "Bargaining in ignorance of the opponent's utility function," Journal of Conflict Resolution, Peace Science Society (International), vol. 6(1), pages 29-38, March.
    21. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    22. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915.
    23. Esther-Mirjam Sent, 2004. "Behavioral Economics: How Psychology Made Its (Limited) Way Back Into Economics," History of Political Economy, Duke University Press, vol. 36(4), pages 735-760, Winter.
    24. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    25. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    26. Joseph B. Kadane & Patrick D. Larkey, 1983. "The Confusion of Is and Ought in Game Theoretic Contexts," Management Science, INFORMS, vol. 29(12), pages 1365-1379, December.
    27. Sanghvi, Arun P., 1978. "Sequential games as stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 323-336, February.
    28. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    29. Innocenti, Alessandro, 1995. "Oskar Morgenstern and the Heterodox Potentialities of the Application of Game Theory to Economics," Journal of the History of Economic Thought, Cambridge University Press, vol. 17(2), pages 205-227, October.
    30. Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
    31. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    32. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    33. Jean-Pierre Ponssard, 1975. "Zero-Sum Games with "Almost" Perfect Information," Management Science, INFORMS, vol. 21(7), pages 794-805, March.
    34. Francesco Guala, 2016. "Understanding Institutions: The Science and Philosophy of Living Together," Economics Books, Princeton University Press, edition 1, number 10742.
    35. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 465-492, April.
    36. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    37. Andrew Colman & Michael Bacharach, 1997. "Payoff Dominance And The Stackelberg Heuristic," Theory and Decision, Springer, vol. 43(1), pages 1-19, July.
    38. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    39. Joseph B. Kadane & Patrick D. Larkey, 1982. "Subjective Probability and the Theory of Games," Management Science, INFORMS, vol. 28(2), pages 113-120, February.
    40. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    41. Andrés Perea, 2014. "From Classical To Epistemic Game Theory," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-22.
    42. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    43. Schotter, Andrew & Schwodiauer, Gerhard, 1980. "Economics and the Theory of Games: A Survey," Journal of Economic Literature, American Economic Association, vol. 18(2), pages 479-527, June.
    44. Joseph B. Kadane & Patrick D. Larkey, 1982. "Reply to Professor Harsanyi," Management Science, INFORMS, vol. 28(2), pages 124-124, February.
    45. H. M. Shefrin, 1981. "Games with Self-Generating Distributions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 511-519.
    46. Marco Mariotti, 1997. "Decisions in games: why there should be a special exemption from Bayesian rationality," Journal of Economic Methodology, Taylor & Francis Journals, vol. 4(1), pages 43-60.
    47. Michael Bacharach, 2006. "The Hi-Lo Paradox, from Beyond Individual Choice: Teams and Frames in Game Theory," Introductory Chapters, in: Natalie Gold & Robert Sugden (ed.),Beyond Individual Choice: Teams and Frames in Game Theory, Princeton University Press.
    48. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    49. Giocoli, Nicola, 2008. "Three alternative (?) stories on the late 20th-century rise of game theory," MPRA Paper 33808, University Library of Munich, Germany.
    50. Shefrin, H. M., 1978. "Differential information and informational equilibrium," Economics Letters, Elsevier, vol. 1(1), pages 33-37.
    51. Shefrin, H. M., 1978. "Differential information and informational equilibrium," Economics Letters, Elsevier, vol. 1(1), pages 15-19.
    52. 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.
    53. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    54. Yaw Nyarko, 2010. "Most games violate the common priors doctrine," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 189-194, March.
    55. John C. Harsanyi, 1982. "Rejoinder to Professors Kadane and Larkey," Management Science, INFORMS, vol. 28(2), pages 124-125, February.
    56. Roger B. Myerson, 2004. "Comments on "Games with Incomplete Information Played by 'Bayesian' Players, I--III Harsanyi's Games with Incoplete Information"," Management Science, INFORMS, vol. 50(12_supple), pages 1818-1824, December.
    57. Mariotti, Marco, 1995. "Is Bayesian Rationality Compatible with Strategic Rationality?," Economic Journal, Royal Economic Society, vol. 105(432), pages 1099-1109, September.
    58. MERTENS, Jean-François & ZAMIR, Shmuel, 1971. "The value of two-person zero-sum repeated games with lack of information on both sides," LIDAM Reprints CORE 154, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    59. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
    60. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
    61. Giocoli, Nicola, 2011. "From Wald to Savage: homo economicus becomes a Bayesian statistician," MPRA Paper 34117, University Library of Munich, Germany.
    62. Hillas, John & Kohlberg, Elon, 2002. "Foundations of strategic equilibrium," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 42, pages 1597-1663, Elsevier.
    63. Shaun Hargreaves Heap & David Rojo Arjona & Robert Sugden, 2014. "How Portable Is Level‐0 Behavior? A Test of Level‐k Theory in Games With Non‐Neutral Frames," Econometrica, Econometric Society, vol. 82(3), pages 1133-1151, May.
    64. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    65. Bernheim, B Douglas, 1986. " Axiomatic Characterizations of Rational Choice in Strategic Environme nts," Scandinavian Journal of Economics, Wiley Blackwell, vol. 88(3), pages 473-488.
    66. Jehoshua Eliashberg, 1981. "An Investigation of Competitive Preference Structures and Posterior Performance Through a Bayesian Decision-Theoretic Approach," Management Science, INFORMS, vol. 27(7), pages 785-801, July.
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    5. Guilhem Lecouteux, 2022. "The Homer economicus narrative: from cognitive psychology to individual public policies," Working Papers hal-03791951, HAL.

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    JEL classification:

    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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