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The Complexity of Exchange


  • Rob Axtell

    () (Brookings Institution and Santa Fe Institute)


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.

Suggested Citation

  • Rob Axtell, 1999. "The Complexity of Exchange," Computing in Economics and Finance 1999 211, Society for Computational Economics.
  • Handle: RePEc:sce:scecf9:211

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