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ESS, Population games, replicator dynamics: dynamics and games if not dynamic games
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.
https://hal.inria.fr/hal-00847275
Contributor : Jean-Luc Gouzé Connect in order to contact the contributor
Submitted on : Tuesday, July 23, 2013 - 11:22:21 AM
Last modification on : Saturday, June 25, 2022 - 11:10:43 PM
Contributor : Jean-Luc Gouzé Connect in order to contact the contributor
Submitted on : Tuesday, July 23, 2013 - 11:22:21 AM
Last modification on : Saturday, June 25, 2022 - 11:10:43 PM
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