Evolution of social behavior in finite populations: A payoff transformation in general -player games and its implications

Kurokawa, Shun; Ihara, Yasuo

doi:10.1016/j.tpb.2012.11.004

Cited by 34 publications

(18 citation statements)

References 21 publications

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“…Finally, we hope that the method presented here can contribute to a more detailed understanding of evolutionary models for multi-player games in finite populations [33,34,35].…”

Section: Discussionmentioning

confidence: 96%

Fitness potentials and qualitative properties of the Wright-Fisher dynamics

Chalub

Souza

2018

Journal of Theoretical Biology

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We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain an expression for the amount of work necessary for a given type to reach fixation. In particular, within this interpretation, we develop a graphical analysis - similar to the one used in classical mechanics - providing the basic tool for a simple heuristic that describes both the short and long term dynamics. As a by-product, we provide a new definition of an evolutionary stable state in finite populations that includes the case of mixed populations. We finish by showing that our theory - rigorous for two types evolution without mutations- is also consistent with the multi-type case, and with the inclusion of rare mutations.

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“…Finally, we hope that the method presented here can contribute to a more detailed understanding of evolutionary models for multi-player games in finite populations [33,34,35].…”

Section: Discussionmentioning

confidence: 96%

Fitness potentials and qualitative properties of the Wright-Fisher dynamics

Chalub

Souza

2018

Journal of Theoretical Biology

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“…Previous studies focus on how mutation, selection and population structure affect these properties of stochastic evolutionary games. However, relatively little work has been done on this issue in the context of multi-player games [26,39,40,[71][72][73]. Motivated by these, we have investigated how the multi-player interaction pattern influences those dynamical properties.…”

Section: Summary and Discussionmentioning

confidence: 99%

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

Traulsen

Gokhale

2013

Games

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William D. Hamilton famously stated that "human life is a many person game and not just a disjoined collection of two person games". However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games.

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“…A multi-player Hawk-Dove game was considered in Broom and Rychtář (2012), and multi-player Public Goods games were considered in a number of papers: Hauert et al (2002), Milinski et al (2006), Santos et al (2008), Ihara (2009), Souza et al (2009), Pacheco (2011), van Veelen andNowak (2012), Kurokawa and Ihara (2013). In order to model this more general type of interaction between individuals, Broom and Rychtář (2012) developed a new framework to analyse multi-player games in networks involving groups of different sizes.…”

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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Evolution of social behavior in finite populations: A payoff transformation in general -player games and its implications

Cited by 34 publications

References 21 publications

Fitness potentials and qualitative properties of the Wright-Fisher dynamics

Fitness potentials and qualitative properties of the Wright-Fisher dynamics

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

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

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