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Perfect Regular Equilibrium

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  • hanjoon michael, jung/j
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    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.

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    File URL: http://mpra.ub.uni-muenchen.de/26534/
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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26534.

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    Date of creation: 09 Oct 2010
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    Handle: RePEc:pra:mprapa:26534

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    Keywords: Bayes' rule; general Multi-period game; Perfect Bayesian equilibrium; Perfect regular equilibrium; Regular conditional probability; Solution concept.;

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    1. Jung, Hanjoon Michael, 2009. "Strategic Information Transmission: Comment," MPRA Paper 17115, University Library of Munich, Germany.
    2. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    3. Jung, Hanjoon Michael, 2009. "Complete Sequential Equilibrium and Its Alternative," MPRA Paper 15443, University Library of Munich, Germany.
    4. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
    5. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
    6. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Kreps, David M & Ramey, Garey, 1987. "Structural Consistency, Consistency, and Sequential Rationality," Econometrica, Econometric Society, vol. 55(6), pages 1331-48, November.
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