title: The replicator equation and other game dynamics.
abstract: The replicator equation is the first and most important game dynamics studied in connection with evolutionary game theory. It was originally developed for symmetric games with finitely many strategies. Properties of these dynamics are briefly summarized for this case, including the convergence to and stability of the Nash equilibria and evolutionarily stable strategies. The theory is then extended to other game dynamics for symmetric games (e.g., the best response dynamics and adaptive dynamics) and illustrated by examples taken from the literature. It is also extended to multiplayer, population, and asymmetric games.
authors.affiliation: Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5; and.
authors.forename: Ross
authors.initials: R
authors.lastname: Cressman
authors.affiliation: Institute of Zoology, Chinese Academy of Sciences, Beijing 1000101, China yitao@ioz.ac.cn.
authors.forename: Yi
authors.initials: Y
authors.lastname: Tao
mesh_terms: D000222:Adaptation, Physiological; D000465:Algorithms; D000818:Animals; D005075:Biological Evolution; D017753:Ecosystem; D005716:Game Theory; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics
keywords: Nash equilibrium; dynamic stability; evolutionarily stable strategy (ESS)