A unified perspective on resource allocation: Limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium, the core and social choice

Abstract

Different forms of resource allocation-by markets, cooperative games, and by social choice - are unified by one condition, limited arbitrage, which is defined on the endowments and the preferences of the traders of an Arrow Debreu economy. Limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium in economies with or without short sales, and with finitely or infinitely many markets. The same condition is also necessary and sufficient for the existence of the core, for resolving Arrow's paradox 011 choices of large utility values, and for the existence of social choice rules which are continuous, anonymous and respect unanimity, thus providing a unified perspective on standard procedures for resource allocation. When limited arbitrage does not hold, social diversity of various degrees is defined by the properties of a topological invariant of the economy, the cohomology rings CH of a family of cones which are naturally associated with it. CH has additional information about the resource allocation properties of subsets of traders in the economy and of the subeconomies which they span.