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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; in revised form: 26 November 2009 / Accepted: 26 November 2009 / Published: 1 December 2009
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.
Keywords: evolutionary game theory; dynamical systems; Nash equilibrium
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MDPI and ACS Style
Sandholm, W.H. Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium. Games 2010, 1, 3-17.
Sandholm WH. Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium. Games. 2010; 1(1):3-17.
Sandholm, William H. 2010. "Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium." Games 1, no. 1: 3-17.