On the equivalence of rational expectations equilibrium with perfect Bayesian equilibrium

A sequential variation of the Arrow-Debreu abstract economy is developed to closely capture the timing of moves of the Walrasian general equilibrium model. Instead of inducing a pseudo- game, the extensive form game of our sequential variation is well defined. It is shown that when information is symmetric, Walrasian equilibrium allocations are equivalent to subgame-perfect equilibrium allocations. When information is asymmetric, rational expectations equilibrium allocations are shown to be equivalent to perfect Bayesian equilibrium allocations. These results are useful for understanding and characterizing Walrasian and rational expectations equilibrium allocations.