The Use of Multiplayer Game Theory in the Modeling of Biological Populations

Broom, Mark

doi:10.1080/08948550302450

Cited by 17 publications

(16 citation statements)

References 40 publications

(46 reference statements)

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“…Yet, another important aspect of most social dilemmas and many other biological examples is that they involve multiple players [5,26,30,45]. [2,3] have made use of the coalescence approach to characterize the mutation process under neutrality and then apply it under weak selection to two-player games with n strategies (n × n).…”

Section: Discussionmentioning

confidence: 99%

Strategy abundance in evolutionary many-player games with multiple strategies

Gokhale

Traulsen

2011

Journal of Theoretical Biology

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Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several parties determines evolutionary success. Rather than pair-wise interactions, in this case we must take into account the interactions between many players, which are inherently more complicated than the usual two-player games, but can still yield simple results. In this manuscript we derive the composition of a many-player multiple strategy system in the mutation-selection equilibrium. This results in a simple expression which can be obtained by recursions using coalescence theory. This approach can be modified to suit a variety of contexts, e.g. to find the equilibrium frequencies of a finite number of alleles in a polymorphism or that of of different strategies in a social dilemma in a cultural context.

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Section: Discussionmentioning

confidence: 99%

Strategy abundance in evolutionary many-player games with multiple strategies

Gokhale

Traulsen

2011

Journal of Theoretical Biology

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“…In order to calculate values of we numerically evaluate, dependent on the number of players, equation (16) (10). The concrete choice of the boundary values is not very relevant since the method is quite robust.…”

Section: Deriving the Diffusion Approximationmentioning

confidence: 99%

“…From multiple bacteria interacting together as in microbiomes [95], in quorum sensing [93] or during biofilm formation [22] to social dilemmas such as the classic tragedy of the commons [40], evolutionary games can be interpreted across scales of organization. For an extensive account for the applications of multiplayer games in biology we refer to Broom [10]. Of interest then, would be a complete eco-evolutionary analysis of fixation probability for multiplayer evolutionary games such that we can understand the e↵ects of demographic changes on the combined eco-evolutionary trajectory.…”

Section: Introductionmentioning

confidence: 99%

Disentangling eco-evolutionary effects on trait fixation

Czuppon

Gokhale

2018

Preprint

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In population genetics, fixation of traits in a demographically changing population under frequencyindependent selection has been extensively analyzed. In evolutionary game theory, models of fixation have typically focused on fixed population sizes and frequency-dependent selection. However, combining ecological fluctuations with frequency-dependent interactions such as Lotka-Volterra dynamics and thus the analysis of eco-evolutionary fixation has received comparatively little attention. Here, we consider a two-type stochastic competitive Lotka-Volterra model with higher order interactions. The emerging individual based model allows for stochastic fluctuations not just in the frequencies of the two types but the total population size as well. Assuming weak selective di↵erences between the traits we approximate the fixation probability for di↵ering competition coe cients. We find that it resembles qualitatively the corresponding evolutionary deterministic dynamics within a population of fixed size. Furthermore, we analyze and partially disentangle the selection e↵ects into their ecological and evolutionary components. Concretely, we show that the evolutionary selection intensity has a larger e↵ect on the predictive power of our approximation than the ecological selection. However, the fixed points themselves are also a↵ected by the selection intensity which implies that a clean separation of the ecological and evolutionary impacts on the evolutionary outcome of the model is not possible. The entanglement of eco-evolutionary processes in a co-evolutionary system is thus a reality which needs to be considered when determining the fixation properties in populations of fluctuating size.

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“…This surprising result for three-player PD contrasts strikingly with our earlier result for two-player PD, played in the same framework, in which even non-factorizable joint probabilities do not result in escaping from the classical consequence of the game.Although multiplayer games have been extensively studied in the game theory literature [1,2] their analysis is often found more complex than for two-player games [3]. Economics [4] and mathematical biology [5][6][7] are the areas where most applications of multiplayer games are discussed.Quantum games first came into prominence following the work of Meyer [8] and Eisert et al [9]. However, the first game-like situations involving many agents were brought to the quantum regime in 1990 by Mermin [10,11].…”

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confidence: 99%

Probabilistic analysis of three-player symmetric quantum games played using the Einstein–Podolsky–Rosen–Bohm setting

2008

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This paper extends our probabilistic framework for two-player quantum games to the mutliplayer case, while giving a unified perspective for both classical and quantum games. Considering joint probabilities in the standard Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting for three observers, we use this setting in order to play general three-player noncooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities provided by the EPR-Bohm setting can change the outcome of a game, while requiring that the quantum game attains a classical interpretation for factorizable joint probabilities. In this framework, our analysis of the three-player generalized Prisoner's Dilemma (PD) shows that the players can indeed escape from the classical outcome of the game, because of nonfactorizable joint probabilities that the EPR setting can provide. This surprising result for three-player PD contrasts strikingly with our earlier result for two-player PD, played in the same framework, in which even non-factorizable joint probabilities do not result in escaping from the classical consequence of the game.Although multiplayer games have been extensively studied in the game theory literature [1,2] their analysis is often found more complex than for two-player games [3]. Economics [4] and mathematical biology [5][6][7] are the areas where most applications of multiplayer games are discussed.Quantum games first came into prominence following the work of Meyer [8] and Eisert et al [9]. However, the first game-like situations involving many agents were brought to the quantum regime in 1990 by Mermin [10,11]. Mermin analyzed a multiplayer game that can be won with certainty when it is played using spin-half particles in a Greenberger-Horne-Zeilinger (GHZ) state [12], while no classical strategy can achieve this.In 1999, Vaidman [13,14] described the GHZ paradox [12] using a game among three players. Vaidman's game is now well known in the quantum game literature. In a similar vein, others [15,16] have discussed game-like situations involving many players for which quantum mechanics significantly helps their chances of winning.The motivation behind these developments [17] was to use a game framework in order to demonstrate the remarkable, and often counterintuitive, quantum correlations that may arise when many agents interact while sharing quantum resources.Systematic procedures were suggested [18-33] to quantize a given game and earlier work considered noncooperative games in their normal-form [1].The approach towards playing quantum games is distinct in that, instead of inventing games in which quantum correlations help players winning games, it proposes quantization procedures for given and very often well known games. That is, instead of tailoring 'winning conditions' for the invented games, which can be satisfied when the game is played by quantum players, quantum game theory finds how the sharing of quantum resources may replace/displace/change the solution(s) or the outcome(s) of known games. The emphasi...

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The Use of Multiplayer Game Theory in the Modeling of Biological Populations

Cited by 17 publications

References 40 publications

Strategy abundance in evolutionary many-player games with multiple strategies

Strategy abundance in evolutionary many-player games with multiple strategies

Disentangling eco-evolutionary effects on trait fixation

Probabilistic analysis of three-player symmetric quantum games played using the Einstein–Podolsky–Rosen–Bohm setting

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