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Perfect Regular Equilibrium

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  • hanjoon michael, jung/j

Abstract

We propose a revised version of the perfect Bayesian equilibrium in general multi-period games with observed actions. In finite games, perfect Bayesian equilibria are weakly consistent and subgame perfect Nash equilibria. In general games that allow a continuum of types and strategies, however, perfect Bayesian equilibria might not satisfy these criteria of rational solution concepts. To solve this problem, we revise the definition of the perfect Bayesian equilibrium by replacing Bayes' rule with a regular conditional probability. We call this revised solution concept a perfect regular equilibrium. Perfect regular equilibria are always weakly consistent and subgame perfect Nash equilibria in general games. In addition, perfect regular equilibria are equivalent to simplified perfect Bayesian equilibria in finite games. Therefore, the perfect regular equilibrium is an extended and simple version of the perfect Bayesian equilibrium in general multi-period games with observed actions.

Suggested Citation

  • hanjoon michael, jung/j, 2010. "Perfect Regular Equilibrium," MPRA Paper 26534, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:26534
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    References listed on IDEAS

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    1. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. Jung, Hanjoon Michael, 2009. "Strategic Information Transmission: Comment," MPRA Paper 17115, University Library of Munich, Germany.
    4. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.
    5. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    6. 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.
    7. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    8. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    9. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-1348, November.
    10. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    11. Jung Hanjoon Michael, 2014. "Comments on “Strategic Information Transmission”," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 1-6, August.
    12. Jung, Hanjoon Michael, 2009. "Complete Sequential Equilibrium and Its Alternative," MPRA Paper 15443, University Library of Munich, Germany.
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    Cited by:

    1. Julio González-Díaz & Miguel Meléndez-Jiménez, 2014. "On the notion of perfect Bayesian equilibrium," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 128-143, April.
    2. Thomas W. L. Norman, 2014. "Sequential Rationality in Continuous No-Limit Poker," Games, MDPI, vol. 5(2), pages 1-5, April.

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    More about this item

    Keywords

    Bayes' rule; general Multi-period game; Perfect Bayesian equilibrium; Perfect regular equilibrium; Regular conditional probability; Solution concept.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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