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Nonlinear and Multiplayer Evolutionary Games

Broom, M. and Rychtar, J. (2016). Nonlinear and Multiplayer Evolutionary Games. Annals of the International Society of Dynamic Games, 14, pp. 95-115. doi: 10.1007/978-3-319-28014-1_5

Abstract

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.

Publication Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-28014-1_5
Publisher Keywords: ESS, Payoffs, Matrix games, Nonlinearity, Multi-player games
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/15851
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