Computing Equilibrium Prices: Does Theory Meet Practice?

  • Bruno Codenotti
  • Benton McCune
  • Rajiv Raman
  • Kasturi Varadarajan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

The best known algorithms for the computation of market equilibria, in a general setting, are not guaranteed to run in polynomial time. On the other hand, simple poly-time algorithms are available for various restricted – yet important – markets.

In this paper, we experimentally explore the gray zone between the general problem and the poly-time solvable special cases. More precisely, we analyze the performance of some simple algorithms, for inputs which are relevant in practice, and where the theory does not provide poly-time guarantees.

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References

  1. 1.
    Arrow, K.J., Debreu, G.: Existence of an Equilibrium for a Competitive Economy. Econometrica 22(3), 265–290 (1954)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Arrow, K.J., Block, H.D., Hurwicz, L.: On the stability of the competitive equilibrium, II. Econometrica 27, 82–109 (1959)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Arrow, K.J., Chenery, H.B., Minhas, B.S., Solow, R.M.: Capital-Labor Substitution and Economic Efficiency. The Review of Economics and Statistics 43(3), 225–250 (1961)CrossRefGoogle Scholar
  4. 4.
    Brooke, A., Kendrick, D., Meeraus, A.: GAMS: A user’s guide. The Scientific Press, South San Francisco (1988)Google Scholar
  5. 5.
    Codenotti, B., Pemmaraju, S., Varadarajan, K.: On the Polynomial Time Computation of Equilibria for Certain Exchange Economies. In: SODA 2005 (2005)Google Scholar
  6. 6.
    Codenotti, B., Pemmaraju, S., Varadarajan, K.: The computation of market equilibria. ACM SIGACT News 35(4), 23–37 (2004)CrossRefGoogle Scholar
  7. 7.
    Codenotti, B., McCune, B., Pemmaraju, S., Raman, R., Varadarajan, K.: An experimental study of different approaches to solve the market equilibrium problem. In: ALENEX 2005 (2005)Google Scholar
  8. 8.
    Codenotti, B., Varadarajan, K.: Efficient Computation of Equilibrium Prices for Markets with Leontief Utilities. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 371–382. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Codenotti, B., McCune, B., Varadarajan, K.: Market Equilibrium via the Excess Demand Function. In: STOC 2005 (2005)Google Scholar
  10. 10.
    Devanur, N.R., Papadimitriou, C.H., Saberi, A., Vazirani, V.V.: Market Equilibrium via a Primal-Dual-Type Algorithm. In: FOCS 2002, pp. 389–395 (2002); Full version with revisions available on line (2003)Google Scholar
  11. 11.
    Dirkse, S.P., Ferris, M.C.: A pathsearch damped Newton method for computing general equilibria. In: Annals of Operations Research, pp. 211–232 (1996)Google Scholar
  12. 12.
    Eaves, B.C., Scarf, H.: The Solution of Systems of Piecewise Linear Equations. Mathematics of Operations Research 1(1), 1–27 (1976)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Eisenberg, E.: Aggregation of Utility Functions. Management Sciences 7(4), 337–350 (1961)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Ferris, M.C., Munson, T.S.: Path 4.6, Available on line at: http://www.gams.com/solvers/path.pdf
  15. 15.
    Ginsburgh, V.A., Waelbroeck, J.L.: Activity Analysis and General Equilibrium Modelling. North-Holland, Amsterdam (1981)MATHGoogle Scholar
  16. 16.
    Gjerstad, S.: Multiple Equilibria in Exchange Economies with Homothetic, Nearly Identical Preference, University of Minnesota, Center for Economic Research, Discussion Paper 288 (1996)Google Scholar
  17. 17.
    Hirota, M.: On the Probability of the Competitive Equilibrium Being Globally Stable: the CES Example, Social Sciences Working Paper 1129, Caltech (2002)Google Scholar
  18. 18.
    Jain, K., Mahdian, M., Saberi, A.: Approximating Market Equilibria. 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
  19. 19.
    Kehoe, T.J.: Computation and Multiplicity of Equilibria. In: Handbook of Mathematical Economics, vol. IV, pp. 2049–2144. North Holland, Amsterdam (1991)Google Scholar
  20. 20.
    Mantel, R.R.: The welfare adjustment process: its stability properties. International Economic Review 12, 415–430 (1971)MATHCrossRefGoogle Scholar
  21. 21.
    Mas-Colell, A., Whinston, M.D., Green, J.R.: Microeconomic Theory. Oxford University Press, Oxford (1995)Google Scholar
  22. 22.
    Negishi, T.: Welfare Economics and Existence of an Equilibrium for a Competitive Economy. Metroeconomica 12, 92–97 (1960)MATHCrossRefGoogle Scholar
  23. 23.
    Papadimitriou, C.H.: On the Complexity of the Parity Argument and other Inefficient Proofs of Existence. Journal of Computer and System Sciences 48, 498–532 (1994)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Scarf, H.: Some Examples of Global Instability of the Competitive Equilibrium. International Economic Review 1, 157–172 (1960)MATHCrossRefGoogle Scholar
  25. 25.
    Scarf, H.: The Approximation of Fixed Points of a Continuous Mapping. SIAM J. Applied Math. 15, 1328–1343 (1967)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Scarf, H.: Comment on “On the Stability of Competitive Equilibrium and the Patterns of Initial Holdings: An Example. International Economic Review 22(2), 469–470 (1981)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Shoven, J.B., Whalley, J.: Applying General Equilibrium. Cambridge University Press, Cambridge (1992)Google Scholar
  28. 28.
    Smale, S.: A convergent process of price adjustment. Journal of Mathematical Economics 3, 107–120 (1976)MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Whalley, J., Zhang, S.: Tax induced multiple equilibria. Working paper, University of Western Ontario (2002)Google Scholar
  30. 30.
    Ye, Y.: A Path to the Arrow-Debreu Competitive Market Equilibrium, Discussion Paper, Stanford University (February 2004); To appear in Mathematical ProgrammingGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bruno Codenotti
    • 1
  • Benton McCune
    • 2
  • Rajiv Raman
    • 2
  • Kasturi Varadarajan
    • 2
  1. 1.Toyota Technological Institute at ChicagoChicago
  2. 2.Department of Computer ScienceThe University of IowaIowa City

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