Buy-Sell Auction Mechanisms in Market Equilibrium

  • Sanjiv Kapoor
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)


In this paper we consider the problem of computing market equilibrium when utilties are homothetic concave functions. We use the Fisher market model. The problem of finding a tâtonnement process for equilibrium in this case has been the subject of recent papers and determining an approximation is of considerable interest. Our buy-sell algorithm starts with an arbitrary price vector and converges to an ε-equilibrium price vector in time proportional to O(1/ε 2). This process attempts to closely mimic the convergence process of real-life markets.


Market Equilibrium Homogeneous Function Excess Demand Price Vector Approximate Optimality 
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  1. 1.
    Arrow, K., Debreu, G.: Existence of an Equilibrium for a Competitive Economy. Econometrica 22, 265–290 (1954)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Codenotti, B., McCune, B., Varadarajan, K.: Market equilibrium via the excess demand function. In: STOC 2005: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, pp. 74–83. ACM Press, New York (2005)CrossRefGoogle Scholar
  3. 3.
    Codenotti, B., Saberi, A., Varadarajan, K., Ye, Y.: Leontief economies encode nonzero sum two-player games. In: SODA 2006: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 659–667. ACM, New York (2006)CrossRefGoogle Scholar
  4. 4.
    Deng, X., Papadimitriou, C., Safra, S.: On the Complexity of Equilibria. In: 34th ACM Symposium on Theory of Computing (STOC 2002), Montreal, Quebec, Canada (May 2002)Google Scholar
  5. 5.
    Devanur, N., Papadimitriou, C., Saberi, A., Vazirani, V.: Market Equilibrium via a Primal-Dual-Type Algorithm. In: 43rd Symposium on Foundations of Computer Science (FOCS 2002), pp. 389–395 (2002); Journal version to appear in the Journal of the ACMGoogle Scholar
  6. 6.
    Fleischer, L., Garg, R., Kapoor, S., Khandekar, R., Saberi, A.: Market equilibrium using indirect utility function. In: WINE (2008)Google Scholar
  7. 7.
    Garg, R., Kapoor, S.: Auction algorithms for market equilibrium. Math. Oper. Res. 31(4), 714–729 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jain, K.: A Polynomial Time Algorithm for Computing the Arrow-Debreau Market equilibrium for Linear Utilities. In: FOCS (2004)Google Scholar
  9. 9.
    Jain, K., Vazirani, V.V., Ye, Y.: Market equilibria for homothetic, quasi-concave utilities and economies of scale in production. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 63–71. Society for Industrial and Applied Mathematics, Philadelphia (2005)Google Scholar
  10. 10.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V. (eds.): Algorithmic Game Theory (2007)Google Scholar
  11. 11.
    Scarf, H.: The approximation of fixed points of a continuous mapping. Siam Journal on Applied Mathematics 15 (1967)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sanjiv Kapoor
    • 1
  1. 1.Illinois Institute of TechnologyChicagoUSA

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