Pairwise Comparison Dynamics and Evolutionary Foundations for Nash Equilibrium
AbstractWe 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.
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Bibliographic InfoArticle provided by MDPI, Open Access Journal in its journal Games.
Volume (Year): 1 (2009)
Issue (Month): 1 (December)
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Web page: http://www.mdpi.com/
evolutionary game theory; dynamical systems; Nash equilibrium;
Find related papers by 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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