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Universally Stable Adjustment Processes - A Unifying Approach

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  • P.J.J. Herings

    (University of Maastricht)

Abstract

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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Bibliographic Info

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
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Web page: http://128.118.178.162

Related research

Keywords: subliminal extant Smith economagic gmm Adjustment processes; game theory; general equilibrium; universal convergence.;

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  1. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  2. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J. & Venniker, R., 1997. "Equilibrium adjustment of disequilibrium prices," Open Access publications from Tilburg University urn:nbn:nl:ui:12-73866, Tilburg University.
  3. 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.
  4. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-31, September.
  5. Judd, Kenneth L., 1997. "Computational economics and economic theory: Substitutes or complements?," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 907-942, June.
  6. Herings, P.J.J., 1994. "A globally and universally stable price adjustment process," Discussion Paper 1994-52, Tilburg University, Center for Economic Research.
  7. 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.
  8. 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.
  9. Van Der Laan, G. & Talman, A. J. J., 1987. "A convergent price adjustment process," Economics Letters, Elsevier, vol. 23(2), pages 119-123.
  10. 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.
  11. 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.
  12. 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.
  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. 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.
  15. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
  16. Kamiya, Kazuya, 1990. "A Globally Stable Price Adjustment Process," Econometrica, Econometric Society, vol. 58(6), pages 1481-85, November.
  17. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
  18. Keenan, Donald, 1981. "Further remarks on the Global Newton method," Journal of Mathematical Economics, Elsevier, vol. 8(2), pages 159-165, July.
  19. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May.
  20. 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, December.
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