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Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium

Author

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  • William H. Sandholm

    () (Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, WI 53706, USA)

Abstract

We introduce a class of evolutionary game dynamics — pairwise comparison dynamics — under which revising agents choose a candidate strategy at random, switching to it with positive probability if and only if its payoff is higher than the agent’s current strategy. We prove that all such dynamics satisfy Nash stationarity : the set of rest points of these dynamics is always identical to the set of Nash equilibria of the underlying game. We also show how one can modify the replicator dynamic and other imitative dynamics to ensure Nash stationarity without increasing the informational demands placed on the agents. These results provide an interpretation of Nash equilibrium that relies on large numbers arguments and weak requirements on payoff observations rather than on strong equilibrium knowledge assumptions.

Suggested Citation

  • William H. Sandholm, 2009. "Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium," Games, MDPI, Open Access Journal, vol. 1(1), pages 1-15, December.
  • Handle: RePEc:gam:jgames:v:1:y:2009:i:1:p:3-17:d:6406
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    Citations

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    Cited by:

    1. Golman, Russell & Page, Scott E., 2010. "Individual and cultural learning in stag hunt games with multiple actions," Journal of Economic Behavior & Organization, Elsevier, vol. 73(3), pages 359-376, March.
    2. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.

    More about this item

    Keywords

    evolutionary game theory; dynamical systems; Nash equilibrium;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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