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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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Suggested Citation

  • P.J.J. Herings, 2001. "Universally Stable Adjustment Processes - A Unifying Approach," GE, Growth, Math methods 0205002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpge:0205002
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    References listed on IDEAS

    as
    1. 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, March.
    2. 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.
    3. Elzen, A. van den & Laan, G. van der & Talman, A.J.J., 1989. "An adjustment process for an exchange economy with linear production technologies," Serie Research Memoranda 0082, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. 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).
    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. 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.
    7. Kamiya, Kazuya, 1990. "A Globally Stable Price Adjustment Process," Econometrica, Econometric Society, vol. 58(6), pages 1481-1485, November.
    8. Van Der Laan, G. & Talman, A. J. J., 1987. "A convergent price adjustment process," Economics Letters, Elsevier, vol. 23(2), pages 119-123.
    9. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    10. 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.
    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. P. Jean-Jacques Herings, 2000. "Two simple proofs of the feasibility of the linear tracing procedure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 485-490.
    13. 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.
    14. Herings, Jean-Jacques & van der Laan, Gerard & Talman, Dolf & Venniker, Richard, 1997. "Equilibrium adjustment of disequilibrium prices," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 53-77, February.
    15. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-563, May.
    16. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
    17. 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.
    18. GĂ©rard Debreu (ed.), 1996. "General Equilibrium Theory," Books, Edward Elgar Publishing, volume 0, number 548.
    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. 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.
    21. Keenan, Donald, 1981. "Further remarks on the Global Newton method," Journal of Mathematical Economics, Elsevier, vol. 8(2), pages 159-165, July.
    22. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-1131, September.
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    24. 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.
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    More about this item

    Keywords

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

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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