Abstract
Perfect Bayesian equilibrium is not a subset of Nash equilibrium. Perfect Bayesian equilibrium requires players to have beliefs that are consistent with the equilibrium strategies of other players. Nash equilibrium does not explicitly specify the beliefs of the players. However, the default beliefs held by players in Nash equilibrium are that the other players are playing the equilibrium strategies (or a particular subset of the equilibrium strategies in the case of multiple equilibriums). The default beliefs and equilibrium strategies in Nash equilibrium could be more narrowly defined than that allowed under Perfect Bayesian equilibrium. Consequently, the set of equilibriums of perfect Bayesian equilibrium is not a subset of Nash equilibrium.
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