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Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium

Andrew McLennan
Hugo Sonnenschein

Abstract

The following characterization of Walrasian allocations is proved: an allocation for an exchange economy with $C^1$ preferences is Walrasian if there is a set of net trades that (i) contains all sums of elements of itself, (ii) contains the negation of any net trade that would improve some agent in the final position, and (iii) is such that the bundles in the allocation are weakly preferred to those obtainable from the initial endowments by means of the given set of net trades. These conditions are similar to ones studied by Schmeidler and Vind (1972) and Vind (1978), but here they are thought of as characterizing the set of net trades available in steady state equilibria of market games like those studied by Douglas Gale (1984, 1985, 1986a, 1986b, and 1986c). The characterization result is used as a key step in the proof of results like Gale's: the allocations induced by steady state equilibria are Walrasian for the economy given by the (constant) flow of new agents into the market. Our approach generalizes the one followed in Gale (1986c) and allows us to dispense with assumptions made in previous treatments. For example Gale's (1986a) assumption of dispersed characteristics is dropped. We also demonstrate that such a result depends on the assumption that agents cannot observe the past behavior of agents with whom they trade.