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Modelling the effects of selection temperature and mutation on the prisoner's dilemma game on a complete oriented star.

Ren J, Xu Y - PLoS ONE (2014)

Bottom Line: This paper models the prisoner's dilemma game based on pairwise comparison in finite populations on a complete oriented star (COS).Then we observe and analyze the effects of two parameters on fixation probability under different population sizes.In particular, it is found through the experimental results that (1) high mutation is more sensitive to the fixation probability than the low one when population size is increasing, while the opposite is the case when the number of cooperators is increasing, and (2) selection temperature demotes the fixation probability.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, Jiangsu Normal University, Xuzhou, China.

ABSTRACT
This paper models the prisoner's dilemma game based on pairwise comparison in finite populations on a complete oriented star (COS). First, we derive a linear system on a COS for calculating the corresponding fixation probabilities that imply dependence of the selection temperature and mutation. Then we observe and analyze the effects of two parameters on fixation probability under different population sizes. In particular, it is found through the experimental results that (1) high mutation is more sensitive to the fixation probability than the low one when population size is increasing, while the opposite is the case when the number of cooperators is increasing, and (2) selection temperature demotes the fixation probability.

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ρm vs N with µ = 1/4000, b = 1.2 and different β values.
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pone-0107417-g007: ρm vs N with µ = 1/4000, b = 1.2 and different β values.

Mentions: Figure 5–8 shows fixation probabilities in the pairwise comparison process under the low mutation rates and high mutation rates and different selection temperatures . Figure 5–6 describes the first-order fixation probability as a function of population size N under the different selection temperatures . Obviously, in Figure 6, there is a slight turning of with the increment of N under small but circumstances turn out to be different in Figure 5, in which is decreasing with N, which accords with a fact: the larger the population size, the more difficultly to taken over it for a single cooperator with given strategy. Figure 7–8 depicts mth-order fixation probability as a function of initial number of cooperators m under the different selection temperatures .  = 0 (red circle) means neutral selection and is given by the fraction of cooperators in Figure 7, which is similar as done in the evolutionary game in well-mixed populations ([26]). However, that is not the case in Figure 8 because of high mutation rates. One can see that with the increment of m, increases in Figure 7, but in Figure 8, only for a high initial number of cooperators, they have reasonable changes. decreases with the increment of if fix N in Figure 7–8.


Modelling the effects of selection temperature and mutation on the prisoner's dilemma game on a complete oriented star.

Ren J, Xu Y - PLoS ONE (2014)

ρm vs N with µ = 1/4000, b = 1.2 and different β values.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4196771&req=5

pone-0107417-g007: ρm vs N with µ = 1/4000, b = 1.2 and different β values.
Mentions: Figure 5–8 shows fixation probabilities in the pairwise comparison process under the low mutation rates and high mutation rates and different selection temperatures . Figure 5–6 describes the first-order fixation probability as a function of population size N under the different selection temperatures . Obviously, in Figure 6, there is a slight turning of with the increment of N under small but circumstances turn out to be different in Figure 5, in which is decreasing with N, which accords with a fact: the larger the population size, the more difficultly to taken over it for a single cooperator with given strategy. Figure 7–8 depicts mth-order fixation probability as a function of initial number of cooperators m under the different selection temperatures .  = 0 (red circle) means neutral selection and is given by the fraction of cooperators in Figure 7, which is similar as done in the evolutionary game in well-mixed populations ([26]). However, that is not the case in Figure 8 because of high mutation rates. One can see that with the increment of m, increases in Figure 7, but in Figure 8, only for a high initial number of cooperators, they have reasonable changes. decreases with the increment of if fix N in Figure 7–8.

Bottom Line: This paper models the prisoner's dilemma game based on pairwise comparison in finite populations on a complete oriented star (COS).Then we observe and analyze the effects of two parameters on fixation probability under different population sizes.In particular, it is found through the experimental results that (1) high mutation is more sensitive to the fixation probability than the low one when population size is increasing, while the opposite is the case when the number of cooperators is increasing, and (2) selection temperature demotes the fixation probability.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, Jiangsu Normal University, Xuzhou, China.

ABSTRACT
This paper models the prisoner's dilemma game based on pairwise comparison in finite populations on a complete oriented star (COS). First, we derive a linear system on a COS for calculating the corresponding fixation probabilities that imply dependence of the selection temperature and mutation. Then we observe and analyze the effects of two parameters on fixation probability under different population sizes. In particular, it is found through the experimental results that (1) high mutation is more sensitive to the fixation probability than the low one when population size is increasing, while the opposite is the case when the number of cooperators is increasing, and (2) selection temperature demotes the fixation probability.

Show MeSH
Related in: MedlinePlus