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2007•RePEc: Research Papers in EconomicsRequires access

A Formal Definition of Perfect Bayesian Equilibrium for Extensive Games

Julio González-Díaz, Miguel A. Meléndez-Jímenez

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Abstract

Often, perfect bayesian equilibrium is loosely defined by stating that players should be sequentially rational given some beliefs in which Bayes rule is applied “whenever possible”. We show that there are games in which it is not clear what “whenever possible” means. Then, we provide a simple definition of perfect bayesian equilibrium for general extensive games that refines both weak perfect equilibrium and subgame perfect equilibrium.

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Often, perfect bayesian equilibrium is loosely defined by stating that players should be sequentially rational given some beliefs in which Bayes rule is applied “whenever possible”. We show that there are games in which it is not clear what “whenever possible” means. Then, we provide a simple definition of perfect bayesian equilibrium for general extensive games that refines both weak perfect equilibrium and subgame perfect equilibrium.

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Available abstract

Often, perfect bayesian equilibrium is loosely defined by stating that players should be sequentially rational given some beliefs in which Bayes rule is applied “whenever possible”. We show that there are games in which it is not clear what “whenever possible” means. Then, we provide a simple definition of perfect bayesian equilibrium for general extensive games that refines both weak perfect equilibrium and subgame perfect equilibrium.

Key concepts: Subgame perfect equilibrium, Sequential equilibrium, Markov perfect equilibrium, Mathematical economics, Bayesian game, Trembling hand perfect equilibrium, Extensive-form game, Bayesian probability

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