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Evolutionary dynamics in finite populations with zealots.

Nakajima Y, Masuda N - J Math Biol (2014)

Bottom Line: We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations.Zealots are assumed to take either strategy regardless of the fitness.We illustrate our results with examples of various social dilemma games.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo , 113-8656, Japan.

ABSTRACT
We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations. Zealots are assumed to take either strategy regardless of the fitness. When the strategy selected by the zealots is the same, the fixation of the strategy selected by the zealots is a trivial outcome. We study fixation time in this scenario. We show that the fixation time is divided into three main regimes, in one of which the fixation time is short, and in the other two the fixation time is exponentially long in terms of the population size. Different from the case without zealots, there is a threshold selection intensity below which the fixation is fast for an arbitrary payoff matrix. We illustrate our results with examples of various social dilemma games.

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Schematic classification of the deterministic dynamics driven by . a–c Populations with zealots. d–g Populations without zealots. Filled and open circles represent stable and unstable equilibria, respectively. Filled squares represent the absorbing boundary condition. It should be noted that we identify
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Fig1: Schematic classification of the deterministic dynamics driven by . a–c Populations with zealots. d–g Populations without zealots. Filled and open circles represent stable and unstable equilibria, respectively. Filled squares represent the absorbing boundary condition. It should be noted that we identify

Mentions: : holds true for all () such that the dynamics starting from any initial condition tends to (Fig. 1a). In an infinite population, dominates . In a finite population, we expect that the fixation time is short. This case occurs when and one of the following conditions is satisfied:


Evolutionary dynamics in finite populations with zealots.

Nakajima Y, Masuda N - J Math Biol (2014)

Schematic classification of the deterministic dynamics driven by . a–c Populations with zealots. d–g Populations without zealots. Filled and open circles represent stable and unstable equilibria, respectively. Filled squares represent the absorbing boundary condition. It should be noted that we identify
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4289535&req=5

Fig1: Schematic classification of the deterministic dynamics driven by . a–c Populations with zealots. d–g Populations without zealots. Filled and open circles represent stable and unstable equilibria, respectively. Filled squares represent the absorbing boundary condition. It should be noted that we identify
Mentions: : holds true for all () such that the dynamics starting from any initial condition tends to (Fig. 1a). In an infinite population, dominates . In a finite population, we expect that the fixation time is short. This case occurs when and one of the following conditions is satisfied:

Bottom Line: We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations.Zealots are assumed to take either strategy regardless of the fitness.We illustrate our results with examples of various social dilemma games.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo , 113-8656, Japan.

ABSTRACT
We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations. Zealots are assumed to take either strategy regardless of the fitness. When the strategy selected by the zealots is the same, the fixation of the strategy selected by the zealots is a trivial outcome. We study fixation time in this scenario. We show that the fixation time is divided into three main regimes, in one of which the fixation time is short, and in the other two the fixation time is exponentially long in terms of the population size. Different from the case without zealots, there is a threshold selection intensity below which the fixation is fast for an arbitrary payoff matrix. We illustrate our results with examples of various social dilemma games.

Show MeSH