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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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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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  1. 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.
  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. 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.
  4. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
  5. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
  6. 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.
  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. 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.
  10. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  11. Van Der Laan, G. & Talman, A. J. J., 1987. "A convergent price adjustment process," Economics Letters, Elsevier, vol. 23(2), pages 119-123.
  12. Kamiya, Kazuya, 1990. "A Globally Stable Price Adjustment Process," Econometrica, Econometric Society, vol. 58(6), pages 1481-85, November.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. Keenan, Donald, 1981. "Further remarks on the Global Newton method," Journal of Mathematical Economics, Elsevier, vol. 8(2), pages 159-165, July.
  18. 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).
  19. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-31, September.
  20. 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.
  21. GĂ©rard Debreu (ed.), 1996. "General Equilibrium Theory," Books, Edward Elgar, volume 0, number 548, March.
  22. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May.
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