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Advances in Dynamic and Evolutionary Games pp 95–115Cite as

Birkhäuser

Nonlinear and Multiplayer Evolutionary Games

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Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 14))

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.

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Authors and Affiliations

  1. Department of Mathematics, City University London, Northampton Square, London, EC1V 0HB, UK

    Mark Broom

  2. Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC, 27412, USA

    Jan Rychtář

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  1. Mark Broom
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  2. Jan Rychtář
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Correspondence to Mark Broom .

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Editors and Affiliations

  1. Dept. of Data Sci. & Know. Eng., Maastricht University, Maastricht, Limburg, The Netherlands

    Frank Thuijsman

  2. Amsterdam School of Economics, Universiteit van Amsterdam, Amsterdam, Noord-Holland, The Netherlands

    Florian Wagener

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Broom, M., Rychtář, J. (2016). Nonlinear and Multiplayer Evolutionary Games. In: Thuijsman, F., Wagener, F. (eds) Advances in Dynamic and Evolutionary Games. Annals of the International Society of Dynamic Games, vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-28014-1_5

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