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Price Roll-Backs and Path Auctions: An Approximation Scheme for Computing the Market Equilibrium

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Internet and Network Economics (WINE 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4286))

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Abstract

In this paper we investigate the structure of prices in approximate solutions to the market equilibrium problem. The bounds achieved allow a scaling approach for computing market equilibrium in the Fisher model. Our algorithm computes an exact solution and improves the complexity of previously known combinatorial algorithms for the problem. It consists of a price roll-back step combined with the auction steps of [11]. Our approach also leads to an efficient polynomial time approximation scheme. We also show a reduction from a flow problem to the market equlibrium problem, illustrating its inherent complexity.

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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., Black, H.D., Hurwicz, L.: On the Stability of the Competetive Equilibrium, II. Economitrica 27, 82–109 (1959)

    Article  MATH  Google Scholar 

  3. Brainard, W.C., Scarf, H.E.: How to Compute Equilibrium Prices in 1891. Cowles Foundation Discussion Paper (1272) (2000)

    Google Scholar 

  4. Codenotti, B., Pemmaraju, S., Varadarajan, K.: A note on the Computation of Equilibria in Exchange Markets with Gross Substitutibility (preprint, 2004)

    Google Scholar 

  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 (November 2002)

    Google Scholar 

  6. Vazirani, V.V., Devanur, N.R.: An Improved Approximation Scheme for Computing the Arrow-Debreu Prices for the Linear Case. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 149–155. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Devanur, N.R., Vazirani, V.V.: The Spending Constraint Model for Market Equilibrium: Algorithmic, Existence and Uniqueness Results. In: Proceedings of the 36th Annual ACM Symposium on the Theory of Computing (2004)

    Google Scholar 

  8. Eaves, B.: A Finite Algorithm for the Linear Exchange Model. Journal of Mathematical Economics 3, 197–203 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  9. Eisenberg, E.: Aggregation of utility functions. Management Sciences 7(4), 337–350 (1961)

    Article  MathSciNet  Google Scholar 

  10. Eisenberg, E., Gale, D.: Consensus of Subjective Probabilities: The Pari-Mutuel Method. Annals of Mathematical Statistics 30, 165–168 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  11. Garg, R., Kapoor, S.: Auction Algorithms for Market Equilibrium. In: Proceedings of the 36th Annual ACM Symposium on the Theory of Computing (2004)

    Google Scholar 

  12. Garg, R., Kapoor, S., Vazirani, V.: An Auction-Based Market Equilbrium Algorithm for the Separable Gross Substitutibility Case. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) RANDOM 2004 and APPROX 2004. LNCS, vol. 3122, Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Jain, K., Mahdian, M., Saberi, A.: Approximating Market Equilibrium. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol. 2764, pp. 98–108. Springer, Heidelberg (2003)

    Google Scholar 

  14. Jain, K.: A Polynomial Time Algorithm for Computing the Arrow-Debreau Market equilibrium for Linear Utilities (preprint)

    Google Scholar 

  15. Nenakov, E.I., Primak, M.E.: One algorithm for finding solutions of the Arrow-Debreu model. Kibernetica 3, 127–128 (1983)

    Google Scholar 

  16. Newman, D.J., Primak, M.E.: Complexity of Circumscribed and Inscribed Ellipsod Methods for Solving Equilibrium Economical Models. Applied Mathematics and Computations 52, 223–231 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Primak, M.E.: A Converging Algorithm for a Linear Exchange Model. Applied Mathematics and Computations 52, 223–231 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  18. Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. J. Comput. Syst. Sci. 26(3), 362–391 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  19. Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  20. Vazirani, V.V.: Market Equilibrium When Buyers Have Spending Constraints (submitted, 2003)

    Google Scholar 

  21. Ye, Y.: A Path to the Arrow-Debreu Competetive Market Equilibrium (preprint, 2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. IBM India Research Lab., New Delhi

    Rahul Garg

  2. Illinois Institute of Technology, Chicago, USA

    Sanjiv Kapoor

Authors
  1. Rahul Garg
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  2. Sanjiv Kapoor
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Editor information

Editors and Affiliations

  1. Department of Computer Engineering and Informatics, University of Patras, 26500, Rio, Patras, Greece

    Paul Spirakis

  2. Department of Computer Science, University of Cyprus, CY-1678, Nicosia, Cyprus

    Marios Mavronicolas

  3. R.A. Computer Technology Institute, N. Kazantzakis Str., University Campus, 26500, Rio–Patra, Greece

    Spyros Kontogiannis

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© 2006 Springer-Verlag Berlin Heidelberg

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Garg, R., Kapoor, S. (2006). Price Roll-Backs and Path Auctions: An Approximation Scheme for Computing the Market Equilibrium. In: Spirakis, P., Mavronicolas, M., Kontogiannis, S. (eds) Internet and Network Economics. WINE 2006. Lecture Notes in Computer Science, vol 4286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944874_21

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  • DOI: https://doi.org/10.1007/11944874_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68138-0

  • Online ISBN: 978-3-540-68141-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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