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Joint Coherence in Games of Incomplete Information

Author

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  • Robert F. Nau

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27706)

Abstract

Decisions are often made under conditions of uncertainty about the actions of supposedly-rational competitors. The modeling of optimal behavior under such conditions is the subject of noncooperative game theory, of which a cornerstone is Harsanyi's formulation of games of incomplete information. In an incomplete-information game, uncertainty may surround the attributes as well as the strategic intentions of opposing players. Harsanyi develops the concept of a Bayesian equilibrium, which is a Nash equilibrium of a game in which the players' reciprocal beliefs about each others' attributes are consistent with a common prior distribution, as though they had been jointly drawn at random from populations with commonly-known proportions of types. The relation of such game-theoretic solution concepts to subjective probability theory and nonstrategic decision analysis has been controversial, as reflected in critiques by Kadane and Larkey and responses from Harsanyi, Shubik, and others, which have appeared in this journal. This paper shows that the Bayesian equilibrium concept and common prior assumption can be reconciled with a subjective view of probability by (i) supposing that players elicit each others' probabilities and utilities through the acceptance of gambles, and (ii) invoking a multi-agent extension of de Finetti's axiom of coherence (no arbitrage opportunities, a.k.a. "Dutch books"). However, the Nash property of statistical independence between players is weakened, and the probability distributions characterizing a solution of the game admit novel interpretations.

Suggested Citation

  • Robert F. Nau, 1992. "Joint Coherence in Games of Incomplete Information," Management Science, INFORMS, vol. 38(3), pages 374-387, March.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:3:p:374-387
    DOI: 10.1287/mnsc.38.3.374
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    Cited by:

    1. repec:ebl:ecbull:v:4:y:2003:i:11:p:1-12 is not listed on IDEAS
    2. Dirk Bergemann & Stephen Morris, 2013. "Bayes Correlated Equilibrium and the Comparison of Information Structures," Levine's Working Paper Archive 786969000000000725, David K. Levine.
    3. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    4. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    5. Marco Scarsini & Yossi Feinberg, 2003. "Rate of Arbitrage and Reconciled Beliefs," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-12.
    6. Leandro Nascimento, 2022. "Bounded arbitrage and nearly rational behavior," Papers 2212.02680, arXiv.org, revised Jul 2023.
    7. Majumdar, Dipjyoti, 2004. "An axiomatic characterization of Bayes' Rule," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 261-273, May.
    8. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
    9. Dirk Bergemann & Stephen Morris, 2011. "Correlated Equilibrium in Games with Incomplete Information," Levine's Working Paper Archive 786969000000000265, David K. Levine.

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