Advances in Dynamic Games pp 291-311

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

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

Chapter

Abstract

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.

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Copyright information

© 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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