Recontracting and competition

We characterize the set of Walrasian allocations of an economy as theset 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 characterizesthe core. The results are extended to production economies by extending thedefinition of the recontracting condition to include the possibility of agentsto recontract with firms. However, no optimization requirement is imposed onfirms. In pure exchange economies, an abstract equilibrium is a feasible allocation and a list of choice sets, one for each agent, that satisfy thefollowing conditions: an agent's choice set is a subset of the commodity space that includes his endowment; and each agent's equilibrium bundle isa maximal element in his choice set, with respect to his preferences. Therecontracting condition requires that any agent can buy bundles from any other agent's choice set by offering the other agent a bundle he prefers tohis equilibrium bundle.