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ESS, Population games, replicator dynamics: dynamics and games if not dynamic games

Pierre Bernhard 1
1 BIOCORE - Biological control of artificial ecosystems
INRA - Institut National de la Recherche Agronomique, CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche
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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https://hal.inria.fr/hal-00847275
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Submitted on : Tuesday, July 23, 2013 - 11:22:21 AM
Last modification on : Friday, June 25, 2021 - 3:36:16 AM

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Pierre Bernhard. ESS, Population games, replicator dynamics: dynamics and games if not dynamic games. Breton, Michèle and Szajowski, Krzysztof. Advances in the Theory and Applications of Dynamic Games, Birkhaüser, pp.291-311, 2011, Annals of the International Society of Dynamic Games, ⟨10.1007/978-0-8176-8089-3_15⟩. ⟨hal-00847275⟩

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