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Continuity Properties of Equilibrium Prices and Allocations in Linear Fisher Markets

  • Nimrod Megiddo
  • Vijay V. Vazirani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4858)

Abstract

Continuity of the mapping from initial endowments and utilities to equilibria is an essential property for a desirable model of an economy – without continuity, small errors in the observation of parameters of the economy may lead to entirely different predicted equilibria.

We show that for the linear case of Fisher’s market model, the (unique) vector of equilibrium prices, Open image in new window is a continuous function of the initial amounts of money held by the agents, Open image in new window , and their utility functions, Open image in new window . Furthermore, the correspondence Open image in new window , giving the set of equilibrium allocations for any specified Open image in new window and Open image in new window , is upper hemicontinuous, but not lower hemicontinuous. However, for a fixed Open image in new window , this correspondence is lower hemicontinuous in Open image in new window .

Keywords

Equilibrium Price Market Model Initial Endowment Unique Maximizer Column Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Arrow, K.J., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Brainard, W.C., Scarf, H.E.: How to compute equilibrium prices in 1891. Cowles Foundation Discussion Paper 1270 (2000)Google Scholar
  3. 3.
    Debreu, G.: Mathematical Economics: Twenty papers of Gerard Debreu. Cambridge University Press, Cambridge (1986)Google Scholar
  4. 4.
    Eisenberg, E., Gale, D.: Consensus of subjective probabilities: the Pari-Mutuel method. The Annals of Mathematical Statistics 30, 165–168 (1959)MathSciNetGoogle Scholar
  5. 5.
    Gale, D.: Theory of Linear Economic Models. McGraw-Hill, New York (1960)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Nimrod Megiddo
    • 1
  • Vijay V. Vazirani
    • 2
  1. 1.IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120 
  2. 2.College of Computing, Georgia Institute of Technology, Atlanta, GA 30332–0280 

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