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Perfect regular equilibrium

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  • Hanjoon Michael Jung

Abstract

We extend the solution concept of perfect Bayesian equilibrium to general games that allow a continuum of types and strategies. In finite games, a perfect Bayesian equilibrium is weakly consistent and a subgame perfect Nash equilibrium. In general games, however, it might not satisfy these criteria. To solve this problem, we revise the definition of perfect Bayesian equilibrium by replacing Bayes’ rule with regular conditional probability. The revised solution concept is referred to as perfect regular equilibrium. We present the conditions that ensure the existence of this equilibrium. Then we show that every perfect regular equilibrium is always weakly consistent and a subgame perfect Nash equilibrium, and is equivalent to a simple version of perfect Bayesian equilibrium in a finite game.

Suggested Citation

  • Hanjoon Michael Jung, 2020. "Perfect regular equilibrium," International Journal of Economic Theory, The International Society for Economic Theory, vol. 16(4), pages 380-398, December.
    • Handle: RePEc:bla:ijethy:v:16:y:2020:i:4:p:380-398
    DOI: 10.1111/ijet.12199
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    References listed on IDEAS

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    6. Jung, Hanjoon Michael, 2009. "Strategic Information Transmission: Comment," MPRA Paper 17115, University Library of Munich, Germany.
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    8. 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.
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    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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    JEL classification:

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

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