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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.

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The steady distribution of investment corresponding to strategy evolution only (Left panel) and that corresponding to coevolution of strategy and investment (Right panel), when σ = 0.8, r = 5.2.From the figure, it can be found that when only strategy is updated, the distribution of the investment in steady state is still a uniform distribution [0.2,1.8], however, when the coevolution of strategy and investment is taken into account, the previous uniform distribution is severely distorted, and the steady investment satisfies a discrete distribution valued [1.786,1.790,1.792,1.793,1.795,1.797,1.798,1.799]. In conclusion, compared to the former case, as the heterogeneity of investment is weakened, the asymptotic fraction of cooperators ρC decreases in the case of coevolution.
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pone.0120317.g005: The steady distribution of investment corresponding to strategy evolution only (Left panel) and that corresponding to coevolution of strategy and investment (Right panel), when σ = 0.8, r = 5.2.From the figure, it can be found that when only strategy is updated, the distribution of the investment in steady state is still a uniform distribution [0.2,1.8], however, when the coevolution of strategy and investment is taken into account, the previous uniform distribution is severely distorted, and the steady investment satisfies a discrete distribution valued [1.786,1.790,1.792,1.793,1.795,1.797,1.798,1.799]. In conclusion, compared to the former case, as the heterogeneity of investment is weakened, the asymptotic fraction of cooperators ρC decreases in the case of coevolution.

Mentions: Comparing the curves in Figs. 2 and 4 leads to the interesting conclusion that the promotion effect of coevolution of strategy and investment is inferior to that of strategy imitation only. With the aim to explore the difference between them, we will discuss the investment distribution of cooperators in steady state. Fig. 5 shows the investment distribution in case of coevolution of strategy and investment (Right panel) and the distribution in case of strategy imitation only (Left panel), and the parameters in the two situations are equal, namely σ = 0.8, r = 5.2. When only strategy evolves with time, the distribution of the investment in steady state is still a uniform distribution [0.2,1.8], which is the same with initial distribution. However, when the coevolution of both strategy and investment is considered, the distribution of investment after evolution comes to an end is severely distorted compared with the uniform distribution at the initial step, and the steady investment satisfies a discrete distribution valued [1.786,1.790,1.792,1.793,1.795,1.797,1.798,1.799]. Therefore, the heterogeneity of investment is weakened in the case of coevolution, leading to the decrement of asymptotic fraction of cooperators ρC. In the same way, through statistical analysis it can be concluded that for the same enhancement r, the smaller the value of σ is, the more severe the distortion from previous uniform distribution will be. This implies that the coevolution of strategy and investment decreases the asymptotic fraction of cooperators ρC by weakening the heterogeneity of investment once again.


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)

The steady distribution of investment corresponding to strategy evolution only (Left panel) and that corresponding to coevolution of strategy and investment (Right panel), when σ = 0.8, r = 5.2.From the figure, it can be found that when only strategy is updated, the distribution of the investment in steady state is still a uniform distribution [0.2,1.8], however, when the coevolution of strategy and investment is taken into account, the previous uniform distribution is severely distorted, and the steady investment satisfies a discrete distribution valued [1.786,1.790,1.792,1.793,1.795,1.797,1.798,1.799]. In conclusion, compared to the former case, as the heterogeneity of investment is weakened, the asymptotic fraction of cooperators ρC decreases in the case of coevolution.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0120317.g005: The steady distribution of investment corresponding to strategy evolution only (Left panel) and that corresponding to coevolution of strategy and investment (Right panel), when σ = 0.8, r = 5.2.From the figure, it can be found that when only strategy is updated, the distribution of the investment in steady state is still a uniform distribution [0.2,1.8], however, when the coevolution of strategy and investment is taken into account, the previous uniform distribution is severely distorted, and the steady investment satisfies a discrete distribution valued [1.786,1.790,1.792,1.793,1.795,1.797,1.798,1.799]. In conclusion, compared to the former case, as the heterogeneity of investment is weakened, the asymptotic fraction of cooperators ρC decreases in the case of coevolution.
Mentions: Comparing the curves in Figs. 2 and 4 leads to the interesting conclusion that the promotion effect of coevolution of strategy and investment is inferior to that of strategy imitation only. With the aim to explore the difference between them, we will discuss the investment distribution of cooperators in steady state. Fig. 5 shows the investment distribution in case of coevolution of strategy and investment (Right panel) and the distribution in case of strategy imitation only (Left panel), and the parameters in the two situations are equal, namely σ = 0.8, r = 5.2. When only strategy evolves with time, the distribution of the investment in steady state is still a uniform distribution [0.2,1.8], which is the same with initial distribution. However, when the coevolution of both strategy and investment is considered, the distribution of investment after evolution comes to an end is severely distorted compared with the uniform distribution at the initial step, and the steady investment satisfies a discrete distribution valued [1.786,1.790,1.792,1.793,1.795,1.797,1.798,1.799]. Therefore, the heterogeneity of investment is weakened in the case of coevolution, leading to the decrement of asymptotic fraction of cooperators ρC. In the same way, through statistical analysis it can be concluded that for the same enhancement r, the smaller the value of σ is, the more severe the distortion from previous uniform distribution will be. This implies that the coevolution of strategy and investment decreases the asymptotic fraction of cooperators ρC by weakening the heterogeneity of investment once again.

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