Computing the arrow-debreu competitive market equilibrium and its extensions

  • Authors:

  • Yinyu Ye

  • Affiliations:

  • Department of Management Science and Engineering, Stanford University, Stanford, CA

  • Venue:
  • AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
  • Year:
  • 2005

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Abstract

We consider the Arrow-Debreu competitive market equilibrium problem which was first formulated by Leon Walras in 1874 [12]. In this problem every one in a population of n players has an initial endowment of a divisible good and a utility function for consuming all goods—own and others. Every player sells the entire initial endowment and then uses the revenue to buy a bundle of goods such that his or her utility function is maximized. Walras asked whether prices could be set for everyone's good such that this is possible. An answer was given by Arrow and Debreu in 1954 [1] who showed that such equilibrium would exist if the utility functions were concave. Their proof was non-constructive and did not offer any algorithm to find such equilibrium prices.