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The Recursive Core

Robert A. Becker
Subir. K. Chakrabarti

Abstract

Core allocations may be defined for infinite horizon capital accumulation models. If agents cannot trust each other in the sense of Gale, then agents may renege on their commitments; their decisions appear time inconsistent. A core allocation is a recursive core allocation provided no coalition can improve upon its consumption stream at any time given its accumulation of assets up to that period. We show for every allocation of consumption in the initial core, one can find a distribution of capital stocks among the agents where no coalition of agents will break the initial core contract at any date. It follows that if the proper distribution of the streams of capital is achieved, then the allocation in the core is also in the recursive core. The latter therefore forges a link between the distribution of wealth (capital), the problem of trust, and time consistent intertemporal contracts.