ESS, population games, replicator dynamics: dynamics and games if not dynamic games.

*(English)* Zbl 1218.91110
Breton, Michèle (ed.) et al., Advances in dynamic games. Theory, applications, and numerical methods for differential and stochastic games. Dedicated to the memory of Arik A. Melikyan. Selected papers presented at the 13th international symposium on dynamic games and applications, Wrocław, Poland, Summer 2008. Boston, MA: Birkhäuser (ISBN 978-0-8176-8088-6/hbk; 978-0-8176-8089-3/ebook). Annals of the International Society of Dynamic Games 11, 291-311 (2011).

Summary: 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.

##### MSC:

91B52 | Special types of equilibria in economics |

91B55 | Economic dynamics |

91A22 | Evolutionary games |