Perfect Regular Equilibrium

October 2010

Perfect Regular Equilibrium*

Hanjoon Michael Jung∙'

The Institute of Economics, Academia Sinica

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.

JEL Classification Number: C72

Keywords: Bayes’ rule, general Multi-period game, Perfect Bayesian equilibrium,

Perfect regular equilibrium, Regular conditional probability, Solution concept.

*I am grateful to Le-Yu Chen and C. C. Yang for their valuable discussions and comments. I would also
like to thank Chia-Hui Chen, Wei-Torng Juang, and Joseph Tao-yi Wang for their helpful suggestions.

I’hc Institute of Economics, Academia Sinica, 128, Sec. 2, Academia Road, Nangang, Taipei 115, Taiwan

i Email address: [email protected]

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