Exchange Processes, the Core and Competitive Allocations

The purpose of this paper is to propose a decentralized resource allocation process for a pure exchange economy that converges from the initial endowments to an allocation in the core of the economy. Being conceived of in a typically non-Walrasian but instead Marshallian spirit, it is inspired from various nontâtonnement, planning and other such processes, for none of which a core convergence property has ever been established. After describing our “exchange process” in Section 2, we introduce in Section 3 the notion of “replicable exchange process” and we prove that any process which is replicable and converges to the core must converge to a competitive allocation. In Section 4 we observe that our exchange process is replicable. We then show that, with the prices it involves, it converges to a competitive equilibrium, hence to an allocation in the core, for the class of economies with quasi-linear utility functions. This restriction is commented upon in the concluding Section 5