Strategy abundance in evolutionary many-player games with multiple strategies

Gokhale, Chaitanya S.; Traulsen, Arne

doi:10.1016/j.jtbi.2011.05.031

Cited by 36 publications

(24 citation statements)

References 48 publications

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“…For 2 × 2 games, the population structure coefficient σ reflects the interaction rate ratio between two patterns of interaction, the interaction of two individuals with the same strategy and that with different strategies [56]. Similarly, σ i depicts the relative interaction rate of the group, in which i co-players have the same strategy as the focal individual [57,58].…”

Section: σ Rule For D-player Gamesmentioning

confidence: 99%

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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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Section: σ Rule For D-player Gamesmentioning

confidence: 99%

“…For a 3-player game for the Moran process with mutations in well mixed population, it has been shown based on coalescence theory that for any mutation probability µ, the abundance of strategy A is greater than one half if and only if (Equation (B.20) in Appendix B in [58])…”

Section: The Moran Process With Mutations In Well Mixed Populationmentioning

confidence: 99%

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

Traulsen

Gokhale

2013

Games

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“…Evolutionary dynamics for strategies in group interactions are complex even in the ideally structureless (well-mixed) populations, with outcomes which cannot be obtained from pairwise interactions [28][29][30]33,34,37,42,43]. In reality, the introduction of not merely multiplayer games but also * longwang@pku.edu.cn structured populations gives rise to polynomial as well as nonlinear fitness functions in evolutionary dynamics [28,29,33,34,38,[44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary dynamics of general group interactions in structured populations

Broom

et al. 2016

Phys. Rev. E

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The evolution of populations is influenced by many factors, and the simple classical models have been developed in a number of important ways. Both population structure and multiplayer interactions have been shown to significantly affect the evolution of important properties, such as the level of cooperation or of aggressive behavior. Here we combine these two key factors and develop the evolutionary dynamics of general group interactions in structured populations represented by regular graphs. The traditional linear and threshold public goods games are adopted as models to address the dynamics. We show that for linear group interactions, population structure can favor the evolution of cooperation compared to the well-mixed case, and we see that the more neighbors there are, the harder it is for cooperators to persist in structured populations. We further show that threshold group interactions could lead to the emergence of cooperation even in well-mixed populations. Here population structure sometimes inhibits cooperation for the threshold public goods game, where depending on the benefit to cost ratio, the outcomes are bistability or a monomorphic population of defectors or cooperators. Our results suggest, counterintuitively, that structured populations are not always beneficial for the evolution of cooperation for nonlinear group interactions.

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“…We note that several authors (e.g., [46,[48][49][50]) have used the stationary distribution as a solution criterion, looking at average abundance of each population type computed by weighting the population states by the stationary distribution. While the authors of this paper find this to be an interesting approach, we use the stationary distribution to measure the stability of particular population states rather than as a measure on individual types.…”

Section: Notions Of Stabilitymentioning

confidence: 99%

Stationary Stability for Evolutionary Dynamics in Finite Populations

Harper¹,

Fryer

2016

Entropy

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Abstract:We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion of stationary stability for the Moran process with mutation and generalizations, as well as a generalized notion of evolutionary stability that includes mutation called an incentive stable state (ISS) candidate. For sufficiently large populations, extrema of the stationary distribution are ISS candidates and we give a family of Lyapunov quantities that are locally minimized at the stationary extrema and at ISS candidates. In various examples, including for the Moran and Wright-Fisher processes, we show that the local maxima of the stationary distribution capture the traditionally-defined evolutionarily stable states. The classical stability theory of the replicator dynamic is recovered in the large population limit. Finally we include descriptions of possible extensions to populations of variable size and populations evolving on graphs.

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Strategy abundance in evolutionary many-player games with multiple strategies

Cited by 36 publications

References 48 publications

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

Evolutionary dynamics of general group interactions in structured populations

Stationary Stability for Evolutionary Dynamics in Finite Populations

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