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Adjustment Dynamics and Rational Play in Games

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Author Info
Jeroen M. Swinkels

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Abstract

When a strategic situation arises repeatedly, the possibility arises that equilibrium predictions can be justified by a dynamic adjustment process. We examine myopic adjustment dynamics, a class that includes replicator dynamics from evolutionary game theory, simple models of imitation, models of experimentation and adjustment, and some simple learning dynamics. We present a series of theorems showing conditions under which behavior that is asymptotically stable under some such dynamic is strategically stable (Kohlberg and Mertens [1986]). This behavior is thus as if the agents in the economy satisfied the extremely stringent assumptions that game theory traditionally makes about rationality and beliefs.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1001.

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Date of creation: Jun 1991
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Handle: RePEc:nwu:cmsems:1001

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Related research
Keywords: game theory; evolution; learning; adjustment dynamics; dynamics; dynamic stability; strategic stability;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  1. Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-90, November. [Downloadable!] (restricted)
  2. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August. [Downloadable!] (restricted)
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  3. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May. [Downloadable!] (restricted)
  4. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  5. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Josef Hofbauer & Jörg Oechssler & Frank Riedel, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Bonn Econ Discussion Papers bgse38_2005, University of Bonn, Germany. [Downloadable!]
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  2. Ulrich Berger & Josef Hofbauer, 2004. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Game Theory and Information 0409002, EconWPA, revised 09 Sep 2004. [Downloadable!]
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  3. Akihiko Matsui & Kiminori Matsuyama, 1991. "An Approach to Equilibrium Selection," Discussion Papers 1065, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  4. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998. [Downloadable!]
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  5. repec:att:wimass:1920221 is not listed on IDEAS
  6. Bill Sandholm, 2003. "Excess Payoff Dynamics, Potential Dynamics, and Stable Games," Theory workshop papers 505798000000000042, UCLA Department of Economics. [Downloadable!]
  7. David K. Levine, 1997. "Learning in the Stock Flow Model," Levine's Working Paper Archive 629, David K. Levine. [Downloadable!]
  8. Sasaki, Yuya, 2004. "The Equivalence Of Evolutionary Games And Distributed Monte Carlo Learning," Economics Research Institute, ERI Series 28338, Utah State University, Economics Department. [Downloadable!]
  9. repec:att:wimass:19199923 is not listed on IDEAS
  10. Demichelis, Stefano & Ritzberger, Klaus & Swinkels, Jeroen M., 2002. "The Simple Geometry of Perfect Information Games," Economics Series 115, Institute for Advanced Studies. [Downloadable!]
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  11. William H. Sandholm, 1997. "An Evolutionary Approach to Congestion," Discussion Papers 1198, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  12. Ken Binmore & Larry Samuelson, . "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
  13. DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On the indices of zeros of nash fields," CORE Discussion Papers 2000017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  14. Ramon Marimon & Ellen McGrattan, 1993. "On Adaptive Learning in Strategic Games," Economics Working Papers 24, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  15. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Max Planck Institute of Economics, Evolutionary Economics Group. [Downloadable!]
  16. DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," CORE Discussion Papers 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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