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Auction algorithms for market equilibrium

Published: 13 June 2004 Publication History

Abstract

In this paper we study algorithms for computing market equilibrium in markets with linear utility functions. The buyers in the market have an initial endowment given by a portfolio of items. The market equilibrium problem is to compute a price vector which ensures market clearing, i. e. the demand of a good equals its supply, and given the prices, each buyer maximizes its utility. The problem is of considerable interest in Economics. This paper presents a formulation of the market equilibrium problem as a parameterized linear program. We construct the dual of these parametrized linear programs. We show that finding the market equilibrium is the same as finding a linear-program from the family of programs where the optimal dual solution satisfies certain properties. The market clearing conditions arise naturally from complementary slackness conditions.We then define an auction mechanism which computes prices such that approximate market clearing is achieved. The algorithm we obtain outperforms previously known methods.

References

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W. C. Brainard and H. E. Scarf. How to compute equilibrium prices in 1891. Cowles Foundation Discussion Paper (1272), 2000.
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X. Deng, C. Papadimitriou, and S. Safra. On the complexity of equilibria. In 34th ACM Symposium on Theory of Computing (STOC 2002), Montreal, Quebec, Canada, May 2002.
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N. R. Devanur and V. Vazirani. An improved approximation scheme for computing the arrow-debreu prices for the linear case. In Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2003), 2003.
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    cover image ACM Conferences
    STOC '04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
    June 2004
    660 pages
    ISBN:1581138520
    DOI:10.1145/1007352
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    Published: 13 June 2004

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    Author Tags

    1. approximation algorithms
    2. auction algorithms
    3. market equilibrium

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    June 13 - 16, 2004
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