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Effect of heterogeneous investments on the evolution of cooperation in spatial public goods game.

Huang K, Wang T, Cheng Y, Zheng X - PLoS ONE (2015)

Bottom Line: Specifically, a large value of the variance of the random variable can decrease the two critical values for the result of behavioral evolution effectively.Moreover, the larger the variance is, the better the promotion effect will be.Comparing the promotion effect of coevolution of strategy and investment with that of strategy imitation only, we can conclude that the coevolution of strategy and investment decreases the asymptotic fraction of cooperators by weakening the heterogeneity of investments, which further demonstrates that heterogeneous investments can promote cooperation in spatial public goods game.

View Article: PubMed Central - PubMed

Affiliation: Department of Automation, Tsinghua University, Beijing, 100084, China.

ABSTRACT
Understanding the emergence of cooperation in spatial public goods game remains a grand challenge across disciplines. In most previous studies, it is assumed that the investments of all the cooperators are identical, and often equal to 1. However, it is worth mentioning that players are diverse and heterogeneous when choosing actions in the rapidly developing modern society and researchers have shown more interest to the heterogeneity of players recently. For modeling the heterogeneous players without loss of generality, it is assumed in this work that the investment of a cooperator is a random variable with uniform distribution, the mean value of which is equal to 1. The results of extensive numerical simulations convincingly indicate that heterogeneous investments can promote cooperation. Specifically, a large value of the variance of the random variable can decrease the two critical values for the result of behavioral evolution effectively. Moreover, the larger the variance is, the better the promotion effect will be. In addition, this article has discussed the impact of heterogeneous investments when the coevolution of both strategy and investment is taken into account. Comparing the promotion effect of coevolution of strategy and investment with that of strategy imitation only, we can conclude that the coevolution of strategy and investment decreases the asymptotic fraction of cooperators by weakening the heterogeneity of investments, which further demonstrates that heterogeneous investments can promote cooperation in spatial public goods game.

Show MeSH
Relationship between asymptotic fraction of cooperators ρC and enhancement factor r corresponding to σ = 0, 0.2, 0.5, 0.8, 1.0 respectively.The curves in the figure show that the larger the value of σ is, the bigger the asymptotic fraction of cooperators ρC will be. In addition, larger value of σ can decrease the values of rC and rD effectively.
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pone.0120317.g002: Relationship between asymptotic fraction of cooperators ρC and enhancement factor r corresponding to σ = 0, 0.2, 0.5, 0.8, 1.0 respectively.The curves in the figure show that the larger the value of σ is, the bigger the asymptotic fraction of cooperators ρC will be. In addition, larger value of σ can decrease the values of rC and rD effectively.

Mentions: While Fig. 1 shows the time series of fraction of cooperators, the relationship between asymptotic fraction of cooperators ρC and enhancement factor r when σ = 0, 0.2, 0.5, 0.8, 1.0 is presented in Fig. 2. It is worth to note that, the black curve in Fig. 2 corresponding to σ = 0 is in agreement with the results in reference [9]. The asymptotic fraction of cooperators ρC depending on the enhancement factor r reveals that ρC is enhanced with increasing of r for different values of σ. Meanwhile, the larger the value of σ is, the bigger the asymptotic fraction of cooperators ρC will be. Besides, a large value of σ will guarantee that the cooperators will survive when the enhancement factor r is small. In addition, for each curve in Fig. 2, there exit two thresholds rC and rD. In other words, if r<rC the phase of the population after behavioral evolution is pure defectors, and if r>rD the phase of the population is pure cooperators, while in case of rC<r<rD the population consist of not only cooperators but also defectors. Fig. 2 clearly demonstrates that larger value of σ can decrease the value of rC and rD effectively. Therefore, to sum up, when the investment of a cooperator is a random variable with uniform distribution [1−σ,1+σ], the asymptotic fraction of cooperators can be promoted. Furthermore, the larger the value of σ is, the better the promotion effect will be.


Effect of heterogeneous investments on the evolution of cooperation in spatial public goods game.

Huang K, Wang T, Cheng Y, Zheng X - PLoS ONE (2015)

Relationship between asymptotic fraction of cooperators ρC and enhancement factor r corresponding to σ = 0, 0.2, 0.5, 0.8, 1.0 respectively.The curves in the figure show that the larger the value of σ is, the bigger the asymptotic fraction of cooperators ρC will be. In addition, larger value of σ can decrease the values of rC and rD effectively.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4363493&req=5

pone.0120317.g002: Relationship between asymptotic fraction of cooperators ρC and enhancement factor r corresponding to σ = 0, 0.2, 0.5, 0.8, 1.0 respectively.The curves in the figure show that the larger the value of σ is, the bigger the asymptotic fraction of cooperators ρC will be. In addition, larger value of σ can decrease the values of rC and rD effectively.
Mentions: While Fig. 1 shows the time series of fraction of cooperators, the relationship between asymptotic fraction of cooperators ρC and enhancement factor r when σ = 0, 0.2, 0.5, 0.8, 1.0 is presented in Fig. 2. It is worth to note that, the black curve in Fig. 2 corresponding to σ = 0 is in agreement with the results in reference [9]. The asymptotic fraction of cooperators ρC depending on the enhancement factor r reveals that ρC is enhanced with increasing of r for different values of σ. Meanwhile, the larger the value of σ is, the bigger the asymptotic fraction of cooperators ρC will be. Besides, a large value of σ will guarantee that the cooperators will survive when the enhancement factor r is small. In addition, for each curve in Fig. 2, there exit two thresholds rC and rD. In other words, if r<rC the phase of the population after behavioral evolution is pure defectors, and if r>rD the phase of the population is pure cooperators, while in case of rC<r<rD the population consist of not only cooperators but also defectors. Fig. 2 clearly demonstrates that larger value of σ can decrease the value of rC and rD effectively. Therefore, to sum up, when the investment of a cooperator is a random variable with uniform distribution [1−σ,1+σ], the asymptotic fraction of cooperators can be promoted. Furthermore, the larger the value of σ is, the better the promotion effect will be.

Bottom Line: Specifically, a large value of the variance of the random variable can decrease the two critical values for the result of behavioral evolution effectively.Moreover, the larger the variance is, the better the promotion effect will be.Comparing the promotion effect of coevolution of strategy and investment with that of strategy imitation only, we can conclude that the coevolution of strategy and investment decreases the asymptotic fraction of cooperators by weakening the heterogeneity of investments, which further demonstrates that heterogeneous investments can promote cooperation in spatial public goods game.

View Article: PubMed Central - PubMed

Affiliation: Department of Automation, Tsinghua University, Beijing, 100084, China.

ABSTRACT
Understanding the emergence of cooperation in spatial public goods game remains a grand challenge across disciplines. In most previous studies, it is assumed that the investments of all the cooperators are identical, and often equal to 1. However, it is worth mentioning that players are diverse and heterogeneous when choosing actions in the rapidly developing modern society and researchers have shown more interest to the heterogeneity of players recently. For modeling the heterogeneous players without loss of generality, it is assumed in this work that the investment of a cooperator is a random variable with uniform distribution, the mean value of which is equal to 1. The results of extensive numerical simulations convincingly indicate that heterogeneous investments can promote cooperation. Specifically, a large value of the variance of the random variable can decrease the two critical values for the result of behavioral evolution effectively. Moreover, the larger the variance is, the better the promotion effect will be. In addition, this article has discussed the impact of heterogeneous investments when the coevolution of both strategy and investment is taken into account. Comparing the promotion effect of coevolution of strategy and investment with that of strategy imitation only, we can conclude that the coevolution of strategy and investment decreases the asymptotic fraction of cooperators by weakening the heterogeneity of investments, which further demonstrates that heterogeneous investments can promote cooperation in spatial public goods game.

Show MeSH