Classical evolutionary game theory has typically considered populations within which randomly selected pairs of individuals play games against each other, and the resulting payoff functions are linear. These simple functions have led to a number of pleasing results for the dynamic theory, the static theory of evolutionarily stable strategies, and the relationship between them. We discuss such games, together with a basic introduction to evolutionary game theory, in Sect. 5.1. Realistic populations, however, will generally not have these nice properties, and the payoffs will be nonlinear. In Sect. 5.2 we discuss various ways in which nonlinearity can appear in evolutionary games, including pairwise games with strategy-dependent interaction rates, and playing the field games, where payoffs depend upon the entire population composition, and not on individual games. In Sect. 5.3 we consider multiplayer games, where payoffs are the result of interactions between groups of size greater than two, which again leads to nonlinearity, and a breakdown of some of the classical results of Sect. 5.1. Finally in Sect. 5.4 we summarise and discuss the previous sections.
ESS Payoffs Matrix games Nonlinearity Multi-player games
91A22 91A06 91A80
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Axelrod R (1981) The emergences of cooperation among egoists. Am Polit Sci Rev 75:306–318CrossRefGoogle Scholar
Ball M, Parker G (2007) Sperm competition games: the risk model can generate higher sperm allocation to virgin females. J Evol Biol 20(2):767–779CrossRefGoogle Scholar
Cannings C (1990) Topics in the theory of ESS’s. In: Lessard S (ed) Mathematical and statistical developments of evolutionary theory. Lecture notes in mathematics, pp 95–119. Kluwer Academic Publishers, DrodrechtCrossRefGoogle Scholar
Cressman R, Křivan V, Garay J (2004) Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments. Am Nat 164(4):473–489CrossRefGoogle Scholar
Cressman R, Křivan V, Brown J, Garay G (2014) Game-theoretic methods for functional response and optimal foraging behavior. PLoS One 9(2):e88773. doi:10.1371/journal.pone.0088773CrossRefGoogle Scholar
Edwards A (2000) Foundations of mathematical genetics. Cambridge University Press, CambridgeMATHGoogle Scholar
Fogel GB, Andrews PC, Fogel DB (1998) On the instability of evolutionary stable strategies in small populations. Ecol Model 109(3):283–294CrossRefGoogle Scholar
Ganzfried S, Sandholm TW (2009) Computing equilibria in multiplayer stochastic games of imperfect information. In: Proceedings of the 21st international joint conference on artificial intelligence (IJCAI)Google Scholar
Geritz S, Kisdi E, Meszéna G, Metz J (1998) Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree. Evol Ecol 12:35–57CrossRefGoogle Scholar
Gokhale C, Traulsen A (2010) Evolutionary games in the multiverse. Proc Natl Acad Sci 107(12):5500–5504CrossRefGoogle Scholar