The Complexity of Exchange

Robert Axtell

No 211, Computing in Economics and Finance 1999 from Society for Computational Economics

Abstract: Recent results on the computational complexity of Brouwer and Kakutani fixed points is reviewed. It is argued that the non-polynomial complexity of fixed-point algorithms makes Walrasian general equilibrium an unrealistic model of real markets. A radically more decentralized and distributed picture of markets involves repeated bilateral trade between agents in a large population. Such bilateral exchange processes converge to equilibrium allocations that are Pareto optimal and are meaningfully viewed as a kind of massively parallel, distributed computation of Pareto optimal allocations. It is proved that bilateral exchange processes are in P , the class of problems that can be solved in polynomial time. The number of bilateral interactions required to reach equilibrium is proportional to AN^2 , where A is the number of agents and N is the number of commodities.

Date: 1999-03-01
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