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Universally Stable Adjustment Processes - A Unifying Approach

  • 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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File URL: http://128.118.178.162/eps/ge/papers/0205/0205002.pdf
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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
Date of revision:
Handle: RePEc:wpa:wuwpge:0205002
Note: Type of Document - pdf.format; pages: 29
Contact details of provider: Web page: http://128.118.178.162

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  1. Keenan, Donald, 1981. "Further remarks on the Global Newton method," Journal of Mathematical Economics, Elsevier, vol. 8(2), pages 159-165, July.
  2. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Venniker, R., 1994. "Equilibrium adjustment of disequilibrium prices," Discussion Paper 1994-84, Tilburg University, Center for Economic Research.
  3. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-31, September.
  4. 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.
  5. Kenneth L. Judd, 1997. "Computational Economics and Economic Theory: Substitutes or Complements," NBER Technical Working Papers 0208, National Bureau of Economic Research, Inc.
  6. 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.
  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, June.
  8. 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.
  9. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
  10. Kamiya, Kazuya, 1990. "A Globally Stable Price Adjustment Process," Econometrica, Econometric Society, vol. 58(6), pages 1481-85, November.
  11. 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.
  12. 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).
  13. 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.
  14. repec:ner:tilbur:urn:nbn:nl:ui:12-73866 is not listed on IDEAS
  15. repec:dgr:kubcen:199777 is not listed on IDEAS
  16. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  17. H. R. Varian, 1976. "A Remark on Boundary Restrictions in the Global Newton Method," Working papers 187, Massachusetts Institute of Technology (MIT), Department of Economics.
  18. repec:ner:tilbur:urn:nbn:nl:ui:12-154936 is not listed on IDEAS
  19. P. Jean-Jacques Herings, 2000. "Two simple proofs of the feasibility of the linear tracing procedure," Economic Theory, Springer, vol. 15(2), pages 485-490.
  20. Yamamoto, Yoshitsugu, 1993. "A Path-Following Procedure to Find a Proper Equilibrium of Finite Games," International Journal of Game Theory, Springer, vol. 22(3), pages 249-59.
  21. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  22. 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.
  23. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May.
  24. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
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