ESS, Population Games, Replicator Dynamics: Dynamics and Games if not Dynamic Games

  • Pierre Bernhard
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 11)


We review some classical definitions and results concerning Evolutionarily Stable Strategies (E.S.S.) with special emphasis on their link to Wardrop equilibrium, and on the nonlinear case where the fitness accrued by an individual depends nonlinearly on the state of the population. On our way, we provide a simple criterion to check that a linear finite dimensional Wardrop equilibrium – or Nash point in the classical E.S.S. literature – satisfies the second-order E.S.S. condition. We also investigate a bifurcation phenomenon in the replicator equation associated with a population game. Finally, we give two nontrivial examples of Wardrop equilibria in problems where the strategies are controls in a dynamic system.


Nash Equilibrium Evolutionary Game Strategy Distribution Stable Strategy Replicator Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of Nice-Sophia AntipolisNiceFrance
  2. 2.INRIA Sophia Antipolis MéditerranéeSophia AntipolisFrance

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