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Games 2010, 1(1), 3-17;

Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium

Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, WI 53706, USA
Received: 15 October 2009 / Revised: 26 November 2009 / Accepted: 26 November 2009 / Published: 1 December 2009
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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. View Full-Text
Keywords: evolutionary game theory; dynamical systems; Nash equilibrium evolutionary game theory; dynamical systems; Nash equilibrium
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Sandholm, W.H. Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium. Games 2010, 1, 3-17.

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