Chapter

Advances in Dynamic Games

Volume 11 of the series Annals of the International Society of Dynamic Games pp 291-311

Date:

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

  • Pierre BernhardAffiliated withUniversity of Nice-Sophia AntipolisINRIA Sophia Antipolis Méditerranée Email author 

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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.