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Universally Stable Adjustment Processes - A Unifying Approach

Listed author(s):
  • P.J.J. Herings

    (University of Maastricht)

Both in game theory and in general equilibrium theory there exists a number of universally stable adjustment processes. In game theory these processes typically serve the role of selecting a Nash equilibrium. Examples are the tracing procedure of Harsanyi and Selten or the equilibrium selection procedure proposed by McKelvey and Palfrey. In general equilibrium the processes are adjustment rules by which an auctioneer can clear all markets. Examples are the processes studied by Smale, Kamiya, van der Laan and Talman, and Herings. The underlying reasons for convergence have remained rather mysterious in the literature, and convergence of different processes has seemed unrelated. This paper shows that convergence of all these processes relies on Browder''s fixed point theorem.

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Paper provided by EconWPA in its series GE, Growth, Math methods with number 0205002.

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Length: 29 pages
Date of creation: 31 Oct 2001
Handle: RePEc:wpa:wuwpge:0205002
Note: Type of Document - pdf.format; pages: 29
Contact details of provider: Web page: http://econwpa.repec.org

References listed on IDEAS
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  1. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Venniker, R., 1997. "Equilibrium adjustment of disequilibrium prices," Other publications TiSEM 22550f27-0bed-4dff-a9de-e, Tilburg University, School of Economics and Management.
  2. McKelvey, Richard D. & Palfrey, Thomas R., 1994. "Quantal Response Equilibria For Normal Form Games," Working Papers 883, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Van Den Elzen, A. & Van Der Laan, G. & Talman, D., 1990. "An Adjustment Process For An Exchange Economy With Linear Production Technologies," Papers 9015, Tilburg - Center for Economic Research.
  4. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
  5. Varian, Hal R., 1977. "A remark on boundary restrictions in the Global Newton method," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 127-130, August.
  6. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
  7. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384.
  8. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
  9. Kenneth L. Judd, 1997. "Computational Economics and Economic Theory: Substitutes or Complements," NBER Technical Working Papers 0208, National Bureau of Economic Research, Inc.
  10. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-1131, September.
  11. Herings P. Jean-Jacques & Peeters R., 1999. "A Differentiable Homotopy to Compute Nash Equilibria of n-Person Games," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  12. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-563, May.
  13. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
  14. van der Laan, G. & Talman, A.J.J., 1987. "A convergent price adjustment process," Other publications TiSEM 0271830c-c03d-46a1-ae6f-f, Tilburg University, School of Economics and Management.
  15. Kamiya, Kazuya, 1990. "A Globally Stable Price Adjustment Process," Econometrica, Econometric Society, vol. 58(6), pages 1481-1485, November.
  16. Herings, Jean-Jacques & van der Laan, Gerard & Venniker, Richard, 1998. "The transition from a Dreze equilibrium to a Walrasian equilibrium1," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 303-330, April.
  17. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
  18. Herings, P.J.J., 1997. "Two Simple Proofs of the Feasibility of the Linear Tracing Procedure," Discussion Paper 1997-77, Tilburg University, Center for Economic Research.
  19. van den Elzen, Antoon, 1997. "An adjustment process for the standard Arrow-Debreu model with production," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 315-324, April.
  20. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  21. Yamamoto, Yoshitsugu, 1993. "A Path-Following Procedure to Find a Proper Equilibrium of Finite Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 249-259.
  22. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
  23. Keenan, Donald, 1981. "Further remarks on the Global Newton method," Journal of Mathematical Economics, Elsevier, vol. 8(2), pages 159-165, July.
  24. Gérard Debreu (ed.), 1996. "General Equilibrium Theory," Books, Edward Elgar Publishing, volume 0, number 548.
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