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Approximating Market Equilibria

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Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques (RANDOM 2003, APPROX 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2764))

Abstract

In this paper we consider the classic problem of finding the market equilibrium prices under linear utility functions. A notion of approximate market equilibrium was proposed by Deng, Papadimitriou and Safra [5]. Using this notion, we present the first fully polynomial-time approximation scheme for finding a market equilibrium price vector. The main tool in our algorithm is the polynomial-time algorithm of Devanur et al. [6] for a variant of the problem in which there is a clear demarcation between buyers and sellers. Their algorithm is used as a subroutine in our algorithm.

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References

  1. Arrow, K., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arrow, K.J., Block, H.D., Hurwicz, L.: On the stability of competitive equilibrium II. Econometrica 27, 82–109 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  3. Arrow, K.J., Hurwicz, L.: On the stability of competitive equilibrium I. Econometrica 26, 522–552 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  4. Brainard, W.C., Scarf, H.E.: How to compute equilibrium prices in 1891. Cowles Foundation Discussion Paper 1270 (2000)

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  5. Deng, X., Papadimitriou, C., Safra, S.: On the complexity of equilibria. In: Proceedings of ACM Symposium on Theory of Computing (2002)

    Google Scholar 

  6. Devanur, N.R., Papadimitriou, C.H., Saberi, A., Vazirani, V.V.: Market equilibrium via a primal-dual-type algorithm. In: The 43rd Annual IEEE Symposium on Foundations of Computer Science (2002)

    Google Scholar 

  7. Gallo, G., Grigoriadis, M.D., Tarjan, R.E.: A fast parametric maximum flow algorithm and applications. SIAM J. Comput. 18(1), 30–55 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kelly, F.P., Vazirani, V.V.: Rate control as a market equilibrium (in preparation)

    Google Scholar 

  9. Papadimitriou, C.H.: Algorithms, games, and the internet. In: Proceedings of ACM Symposium on Theory of Computing (2001)

    Google Scholar 

  10. Scarf, H.: The Computation of Economic Equilibria (with collaboration of T. Hansen). Cowles Foundation Monograph 24. Yale University Press, New Haven (1973)

    Google Scholar 

  11. Wald, A.: On some systems of equations of mathematical economics. Zeitschrift für Nationalökonomie 7 (1936); Translated, 1951, Econometrica 19(4), pp. 368–403

    Google Scholar 

  12. Walras, L.: Éléments d’économie politique pure; ou. Théorie de la richesse sociale (Elements of Pure Economics, or the theory of social wealth), Lausanne, Paris (1874) (1899, 4th ed.; 1926, rev ed., 1954, Engl. transl.)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA, 98052, USA

    Kamal Jain

  2. Laboratory for Computer Science, MIT, Cambridge, MA, 02139, USA

    Mohammad Mahdian

  3. College of Computing, Georgia Tech, Atlanta, GA, 30332, USA

    Amin Saberi

Authors
  1. Kamal Jain
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  2. Mohammad Mahdian
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  3. Amin Saberi
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Editor information

Editors and Affiliations

  1. Computer Science Department, Princeton University, 35 Olden Street, 08540, Princeton, NJ

    Sanjeev Arora

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Battelle Bâtiment A, Centre Universitaire d’Informatique, Route de Drize 7, 1227, Carouge, Geneva, Switzerland

    José D. P. Rolim

  4. University of California, Los Angeles

    Amit Sahai

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© 2003 Springer-Verlag Berlin Heidelberg

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Jain, K., Mahdian, M., Saberi, A. (2003). Approximating Market Equilibria. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds) Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques. RANDOM APPROX 2003 2003. Lecture Notes in Computer Science, vol 2764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45198-3_9

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  • DOI: https://doi.org/10.1007/978-3-540-45198-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40770-6

  • Online ISBN: 978-3-540-45198-3

  • eBook Packages: Springer Book Archive

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