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Competitive equilibria in pure exchange economies are characterized without assuming the apriori existence of a price system and price taking behavior. It is assumed that every agent chooses an optimal bundle from a choice set of feasible bundles, that includes the agent's endowment. In addition it is required that every agent's choice set includes all bundles that result from buying a bundle from any other agent's chice set in exchange to a bundle that the other agent prefers to his equilibrium bundle. The result is that the allocations supported by such equilibria are competitive.

An interpretation of the characterization is that "price taking behavior" is replaced by the weaker requirement of "choice sets taking behavior", together with the requirement that there is no advantage for agents from trading directly with each other, as all such possible gains of trade are already included in the choice sets.

The result is closely related to Debreu and Scarf's (1963) limit theorem of the core of a replicated economy. In addition, it is possible to characterize the core by similar weaker conditions.

We characterize the set of Walrasian allocations of an economy as the set of allocations which can be supported by abstract equilibria that satisfy a recontracting condition which reflects the idea that agents can freely trade with each other. An alternative (and weaker) recontracting condition characterizes the core. The results are extended to production economies by extending the definition of the recontracting condition to include the possibility of agents to recontract with firms. However, no optimization requirement is imposed on firms. In pure exchange economies, an abstract equilibrium is a feasible allocation and a list of choice sets, one for each agent, that satisfy the following conditions: an agent's choice set is a subset of the commodity space that includes his endowment; and each agent's equilibrium bundle is a maximal element in his choice set, with respect to his preferences. The recontracting condition requires that any agent can buy bundles from any other agent's choice set by offering the other agent a bundle he prefers to his equilibrium bundle.

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- Darin Lee,
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