Evolutionary Drift and Equilibrium Selection

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Evolutionary Drift and Equilibrium Selection

Author Info

Ken Binmore
Larry Samuelson

Abstract

This paper develops an approach to equilibrium selection in game theory based on studying the equilibriating process through which equilibrium is achieved. The differential equations derived from models of interactive learning typically have stationary states that are not isolated. Instead, Nash equilibria that specify the same behavior on the equilibrium path, but different out-of-equilibrium behavior, appear in connected components of stationary states. The stability properties of these components often depend critically on the perturbations to which the system is subjected. We argue that it is then important to incorporate such drift into the model. A suffcient condition is provided for drift to create stationary states with strong stability properties near a component of equilibria. This result is used to derive comparative static predictions concerning common questions raised in the literature on refinements of Nash equilibrium

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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 011.

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Find related papers by JEL classification:
C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
Other versions:
- Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
- Samuelson, L. & Zhang, J., 1990. "Evolutionary Stability In Symmetric Games," Working papers 90-24, Wisconsin Madison - Social Systems.
Boylan Richard T., 1995. "Continuous Approximation of Dynamical Systems with Randomly Matched Individuals," Journal of Economic Theory, Elsevier, vol. 66(2), pages 615-625, August. [Downloadable!] (restricted)
repec:att:wimass:199517r is not listed on IDEAS
Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August. [Downloadable!] (restricted)
Other versions:
- FUDENBERG, Drew & HARRIS, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers 13, Institut d'Économie Industrielle (IDEI), Toulouse.
Guth, Werner & Tietz, Reinhard, 1990. "Ultimatum bargaining behavior : A survey and comparison of experimental results," Journal of Economic Psychology, Elsevier, vol. 11(3), pages 417-449, September. [Downloadable!] (restricted)
van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August. [Downloadable!] (restricted)
Other versions:
- van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July. [Downloadable!] (restricted)
Mailath, G.J. & Samuelson, L. & Swinkels, J., 1990. "Extensive Form Reasoning In Normal Games," Papers 43, Princeton, Woodrow Wilson School - Discussion Paper.
repec:att:wimass:199325 is not listed on IDEAS
Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December. [Downloadable!] (restricted)
Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September. [Downloadable!] (restricted)
Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December. [Downloadable!] (restricted)
Other versions:
- Drew Fudenberg & Eddie Dekel, 1987. "Rational Behavior with Payoff Uncertainty," Working papers 471, Massachusetts Institute of Technology (MIT), Department of Economics.
Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November. [Downloadable!] (restricted)
Binmore, Ken, and Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Discussion Paper Serie B 275, University of Bonn, Germany.
Other versions:
- Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA. [Downloadable!]
- Ken Binmore & Larry Samuelson, 1994. "Muddling Through:Noisy Equilibrium Selection," Game Theory and Information 9403005, EconWPA, revised 29 Mar 1994. [Downloadable!]
repec:att:wimass:199323 is not listed on IDEAS
repec:att:wimass:199324 is not listed on IDEAS
Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August. [Downloadable!] (restricted)
Other versions:
- Paul Milgrom & John Roberts, 1997. "Predation, reputation , and entry deterrence," Levine's Working Paper Archive 1460, UCLA Department of Economics. [Downloadable!]
- Paul Milgrom & John Roberts, 1980. "Predation, Reputation, and Entry Deterrence," Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July. [Downloadable!] (restricted)
Other versions:
- Jeroen M. Swinkels, 1991. "Adjustment Dynamics and Rational Play in Games," Discussion Papers 1001, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Antonio Cabrales, 1993. "Stochastic Replicator Dynamics," Economics Working Papers 54, Department of Economics and Business, Universitat Pompeu Fabra.
Other versions:
- Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-81, May.
Bolton, Gary E, 1991. "A Comparative Model of Bargaining: Theory and Evidence," American Economic Review, American Economic Association, vol. 81(5), pages 1096-136, December. [Downloadable!] (restricted)
Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
Ochs, Jack & Roth, Alvin E, 1989. "An Experimental Study of Sequential Bargaining," American Economic Review, American Economic Association, vol. 79(3), pages 355-84, June. [Downloadable!] (restricted)
Akihiko Matsui, 1989. "Cheap Talk and Cooperation in the Society," Discussion Papers 848, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer, vol. 23(3), pages 207-36.
Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August. [Downloadable!] (restricted)
Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August. [Downloadable!] (restricted)
Yong Gwan Kim & Joel Sobel, 1992. "An Evolutionary Approach to Pre-Play Communication," University of California at San Diego, Economics Working Paper Series 92-01, Department of Economics, UC San Diego.
Other versions:
- Kim, Y.G. & Sobel, J., 1993. "An Evolutionary Approach to Pre-Play Communication," Working Papers 93-02, University of Iowa, Department of Economics.
- Kim, Yong-Gwan & Sobel, Joel, 1995. "An Evolutionary Approach to Pre-play Communication," Econometrica, Econometric Society, vol. 63(5), pages 1181-93, September. [Downloadable!] (restricted)
Blume Andreas & Kim Yong-Gwan & Sobel Joel, 1993. "Evolutionary Stability in Games of Communication," Games and Economic Behavior, Elsevier, vol. 5(4), pages 547-575, October. [Downloadable!] (restricted)
Other versions:
- Blume, A. & Kim, Y.G. & Sobel, J., 1992. "Evolutionary Stability in Games of Communication," Working Papers 92-17, University of Iowa, Department of Economics.
- Andreas Blume & Yong-Gwan Kim & Joel Sobel, 1992. "Evolutionary Stability in Games of Communication," University of California at San Diego, Economics Working Paper Series 92-29, Department of Economics, UC San Diego.
- Blume, A. & Kim, Y.G. & Sobel, J., 1993. "Evolutionary Stability in Games of Communication," Working Papers 93-07, University of Iowa, Department of Economics.
Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August. [Downloadable!] (restricted)
Balkenborg, Dieter, 1994. "An Experiment on Forward- versus Backward Induction," Discussion Paper Serie B 268, University of Bonn, Germany.
Schlag,Karl, . "Dynamic stability in the repeated prisoners dilemma," Discussion Paper Serie B 243, University of Bonn, Germany.

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Rod Garratt & Thomas Troger, 2003. "Speculation in Second-Price Auctions with Resale," University of California at Santa Barbara, Economics Working Paper Series wp4-03, Department of Economics, UC Santa Barbara. [Downloadable!]
Other versions:
- Rod Garratt & Thomas Troger, 2003. "Speculation in Second-Price Auctions with Resale," Game Theory and Information 0305003, EconWPA. [Downloadable!]
- Rod Garratt & Thomas Troger, 2003. "Speculation in Second-Price Auctions with Resale," Levine's Bibliography 506439000000000246, UCLA Department of Economics. [Downloadable!]
Stefano Demichelis & Jörgen W. Weibull, 2007. "Language, meaning and games: a model of communication, coordination and evolution," Carlo Alberto Notebooks 61, Collegio Carlo Alberto. [Downloadable!]

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