Wang Jing, Wu Bin, Chen Xiaojie, Wang Long
Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May;81(5 Pt 2):056103. doi: 10.1103/PhysRevE.81.056103. Epub 2010 May 12.
The public goods game is a powerful metaphor for exploring the maintenance of social cooperative behavior in a group of interactional selfish players. Here we study the emergence of cooperation in the public goods games with diverse contributions in finite populations. The theory of stochastic process is innovatively adopted to investigate the evolutionary dynamics of the public goods games involving a diversity of contributions. In the limit of rare mutations, the general stationary distribution of this stochastic process can be analytically approximated by means of diffusion theory. Moreover, we demonstrate that increasing the diversity of contributions greatly reduces the probability of finding the population in a homogeneous state full of defectors. This increase also raises the expectation of the total contribution in the entire population and thus promotes social cooperation. Furthermore, by investigating the evolutionary dynamics of optional public goods games with diverse contributions, we find that nonparticipation can assist players who contribute more in resisting invasion and taking over individuals who contribute less. In addition, numerical simulations are performed to confirm our analytical results. Our results may provide insight into the effect of diverse contributions on cooperative behaviors in the real world.
公共物品博弈是一种强大的隐喻，用于探索在一群相互作用的自私参与者中社会合作行为的维持。在此，我们研究了在有限群体中具有不同贡献的公共物品博弈中合作的出现。创新性地采用随机过程理论来研究涉及多种贡献的公共物品博弈的进化动态。在罕见突变的极限情况下，该随机过程的一般平稳分布可以通过扩散理论进行解析近似。此外，我们证明，增加贡献的多样性会大大降低在充满背叛者的同质状态中发现群体的概率。这种增加还提高了整个人口中总贡献的期望，从而促进了社会合作。此外，通过研究具有不同贡献的可选公共物品博弈的进化动态，我们发现不参与可以帮助贡献更多的参与者抵抗入侵并取代贡献较少的个体。此外，进行了数值模拟以证实我们的分析结果。我们的结果可能为不同贡献对现实世界中合作行为的影响提供见解。
