Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation

Ladret, Véronique; Lessard, Sabin

doi:10.1016/j.jtbi.2008.07.025

Cited by 13 publications

(36 citation statements)

References 26 publications

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“…We also plot the critical value of b/c above which cooperators achieve a higher payoff in M total rounds, on average, than do defectors if f = 2/3 (red squares) for m = 8 and m = 16. The two sets of data points agree well, as we would expect from the one-third law of evolutionary dynamics [2,[47][48][49][50][51]. In addition, we show the functions A(2/3, 8; p) and A(2/3, 16; p).…”

Section: Simulation Resultssupporting

confidence: 79%

Indirect Reciprocity with Optional Interactions and Private Information

Olejarz

Ghang

Nowak

2015

Games

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We consider indirect reciprocity with optional interactions and private information. A game is offered between two players and accepted unless it is known that the other person is a defector. Whenever a defector manages to exploit a cooperator, his or her reputation is revealed to others in the population with some probability. Therefore, people have different private information about the reputation of others, which is a setting that is difficult to analyze in the theory of indirect reciprocity. Since a defector loses a fraction of his social ties each time he exploits a cooperator, he is less efficient at exploiting cooperators in subsequent rounds. We analytically calculate the critical benefit-to-cost ratio above which cooperation is successful in various settings. We demonstrate quantitative agreement with simulation results of a corresponding Wright-Fisher process with optional interactions and private information. We also deduce a simple necessary condition for the critical benefit-to-cost ratio.

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Section: Simulation Resultssupporting

confidence: 79%

Indirect Reciprocity with Optional Interactions and Private Information

Olejarz

Ghang

Nowak

2015

Games

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“…This result is an instance of the one-third law of evolutionary game theory Ohtsuki et al, 2007;Bomze and Pawlowitsch, 2008;Ladret and Lessard, 2008;Zheng et al, 2011). This rule can be understood as stating that the conditionsf (1/3) > 1 and ρ A > 1/N are equivalent up to borderline cases.…”

Section: Discussionmentioning

confidence: 89%

“…In the wN limit, we find in Theorem 2 (see also Bomze and Pawlowitsch, 2008) that a + 2b > c + 2d is sufficient for ρ A > 1/N, and is necessary except in the borderline case a + 2b = c + 2d. This result is an instance of the one-third law of evolutionary game theory (Nowak et al, 2004;Ohtsuki et al, 2007;Bomze and Pawlowitsch, 2008;Ladret and Lessard, 2008;Zheng et al, 2011). This rule can be understood as stating that the conditions f (1/3) > 1 and ρ A > 1/N are equivalent up to borderline cases.…”

Section: Discussionmentioning

confidence: 90%

The limits of weak selection and large population size in evolutionary game theory

Sample

Allen

2017

J. Math. Biol.

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Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the wN limit, in which weak selection is applied before the large population limit, and the N w limit, in which the order is reversed. Formal mathematical definitions of the N w and wN limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the N w and wN limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.

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“…The approach of studying fixation probabilities via first-order expansions, as in Eq. ( 17), also appears in [63], [32], and [31]. The proof of Eq.…”

Section: 21mentioning

confidence: 84%

Fixation Probabilities for Any Configuration of Two Strategies on Regular Graphs

Chen

McAvoy

Nowak

2016

Sci Rep

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Population structure and spatial heterogeneity are integral components of evolutionary dynamics, in general, and of evolution of cooperation, in particular. Structure can promote the emergence of cooperation in some populations and suppress it in others. Here, we provide results for weak selection to favor cooperation on regular graphs for any configuration, meaning any arrangement of cooperators and defectors. Our results extend previous work on fixation probabilities of rare mutants. We find that for any configuration cooperation is never favored for birth-death (BD) updating. In contrast, for death-birth (DB) updating, we derive a simple, computationally tractable formula for weak selection to favor cooperation when starting from any configuration containing any number of cooperators. This formula elucidates two important features: (i) the takeover of cooperation can be enhanced by the strategic placement of cooperators and (ii) adding more cooperators to a configuration can sometimes suppress the evolution of cooperation. These findings give a formal account for how selection acts on all transient states that appear in evolutionary trajectories. They also inform the strategic design of initial states in social networks to maximally promote cooperation. We also derive general results that characterize the interaction of any two strategies, not only cooperation and defection.

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Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation

Cited by 13 publications

References 26 publications

Indirect Reciprocity with Optional Interactions and Private Information

Indirect Reciprocity with Optional Interactions and Private Information

The limits of weak selection and large population size in evolutionary game theory

Fixation Probabilities for Any Configuration of Two Strategies on Regular Graphs

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