Evolutionary and asymptotic stability in symmetric multi-player games

Bukowski, Maciej; Miękisz, Jacek

doi:10.1007/s001820400183

Cited by 60 publications

(53 citation statements)

References 17 publications

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“…Thus it is natural to generalise evolutionary games to more than two individuals. Multi-player games were introduced into biology in Palm (1984) and the theory developed by Broom et al (1997), see also Bukowski and Miekisz (2004). (b) Fig.…”

Section: Modelling Structured Populations With Multi-player Interactionsmentioning

confidence: 99%

A study of the dynamics of multi-player games on small networks using territorial interactions

et al. 2015

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Citation: Broom, M., Lafaye, C., Pattni, K. & Rychtar, J. (2015). A study of the dynamics of multi-player games on small networks using territorial interactions.. Journal of Mathematical Biology, doi: 10.1007/s00285-015-0868-1 This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract Recently, the study of structured populations using models of evolutionary processes on graphs has begun to incorporate a more general type of interaction between individuals, allowing multi-player games to be played among the population. In this paper, we develop a birth-death dynamics for use in such models and consider the evolution of populations for special cases of very small graphs where we can easily identify all of the population states and carry out exact analyses. To do so, we study two multi-player games, a Hawk-Dove game and a public goods game. Our focus is on finding the fixation probability of an individual from one type, cooperator or defector in the case of the public goods game, within a population of the other type. We compare this value for both games on several graphs under different parameter values and assumptions, and identify some interesting general features of our model. In particular there is a very close relationship between the fixation probability and the mean temperature, with high temperatures helping fitter individuals and punishing unfit ones and so enhancing selection, whereas low temperatures give a levelling effect which suppresses selection. Permanent

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Section: Modelling Structured Populations With Multi-player Interactionsmentioning

confidence: 99%

A study of the dynamics of multi-player games on small networks using territorial interactions

et al. 2015

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“…However until recently they have been less common in evolutionary games. An extension of the classical idea of well-mixed populations of pairwise games to consider such populations with multiplayer games was first introduced with the work of Palm (1984) and followed by Haigh and Cannings (1989) ;Broom et al (1997); Bukowski and Miȩkisz (2004). More recently Hauert et al (2006), Gokhale and Traulsen (2010), Han et al (2012), Gokhale and Traulsen (2014) have developed the theory further.…”

Section: Discussionmentioning

confidence: 99%

“…For a proof see Broom et al (1997) or Bukowski and Miȩkisz (2004). A strategy p is an ESS at level J if, for every q = p, the conditions (48-49) of Theorem 6 are satisfied for some j ≤ J and there is at least one q = p for which the conditions are met for j = J precisely.…”

Section: Esss In Multi-player Matrix Gamesmentioning

confidence: 99%

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Nonlinear and Multiplayer Evolutionary Games

Broom

Rychtář

2016

Advances in Dynamic and Evolutionary Games

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This is the accepted version of the paper.This version of the publication may differ from the final published version. 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 Section 1. Realistic populations, however, will generally not have these nice properties, and the payoffs will be nonlinear. In Section 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 Section 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 Section 1. Finally in Section 4 we summarise and discuss the previous sections. Permanent repository link

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“…Only recently there have appeared some systematic studies of truly multiplayer games [13,14,15]. Here we consider spatial games with players located on vertices of the triangular lattice.…”

Section: Introductionmentioning

confidence: 99%