The Perfect Bayesian equilibrium is not a refinement of the Nash equilibrium. The Perfect Bayesian equilibrium requires players to have beliefs that are consistent with the equilibrium strategies of other players. The Nash equilibrium does not explicitly specify the beliefs of the players. In any given Nash equilibrium, the default beliefs held by players 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 those allowed under Perfect Bayesian equilibrium. Consequently, the set of equilibriums under Perfect Bayesian equilibrium is not a subset of the set of equilibriums under Nash equilibrium.