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Existence and Characterization of Perfect Equilibrium in Games of Perfect Information

Econometrica 1985 53(3), 613
[The existence of perfect equilibrium is demonstrated for a class of games with compact space of histories and continuous payoffs, and in which the set of actions feasible at any given period is a lower hemicontinuous correspondence of the previous history of the game. The proof is by construction. A set of histories is constructed, each of which is the equilibrium path of some perfect equilibrium point of the game. Also, any equilibrium path is a member of this set. The construction therefore provides a characterization of perfect equilibrium.]

Voluntary and Efficient Allocations are Walrasian

Econometrica 1985 53(4), 807
Let F be a private ownership economy. Call an allocation w for a price vector p if no agent can benefit by trading less at p. We prove that, under differentiability and interiority, if w is voluntary and Pareto efficient it is a competitive equilibrium for W. Perhaps surprisingly, production economies where some agents receive profit income require a stronger voluntariness condition than the one sufficient for exchange economies. The stronger condition singles out a commodity as a medium of exchange.