Perfect regular equilibrium

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.