On the equivalence of rational expectations equilibrium with perfect Bayesian equilibrium
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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.
KeywordsAbstract economy Perfect Bayesian equilibrium Rational expectations equilibrium Subgame-perfect equilibrium Walrasian equilibrium
JEL ClassificationD50 D51
We gratefully acknowledge helpful comments and suggestions from Zhiwei Liu, Xinxi Song, and participants at 2017 Nanjing International Conference on Game Theory and the Fourth Microeconomics Workshop, 2018 SAET Conference, and 2018 ISEM Workshop on Economics and Finance. We are also very grateful to Dionysius Glycopantis, the editor, and a referee for their constructive comments and suggestions that have greatly improved the paper. Financial support from the National Natural Science Foundation of China (Grant No. 71472110) is gratefully acknowledged.
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