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中国物理学会期刊

具有异质增益因子的超图上的演化公共品博弈

CSTR: 32037.14.aps.70.20212436

Evolutionary public goods games on hypergraphs with heterogeneous multiplication factors

CSTR: 32037.14.aps.70.20212436
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  • 近年来, 空间结构和社会多样性对群体合作演化的影响吸引了人们极大的关注. 本文在空间公共品博弈中引入了异质增益因子, 研究超图上合作行为的演化. 除所有博弈群组具有相同增益因子的原始模型外, 还考虑了包括均匀分布、指数分布和幂律分布在内的不同异质性强度的三类异质增益因子分布. 数值模拟结果显示, 上述4种增益因子分布对应的公共品博弈中, 均匀随机超图阶数g的增大有利于提高群体的合作水平. 更进一步地, 对比超图上原始空间公共品博弈的演化结果, 群体中博弈群组增益因子异质性的引入能够显著促进群体的合作行为, 幂律分布情况下能够使得系统获得最高合作水平. 此外, 研究了超边数目对群体合作演化的影响, 结果表明上述结论对超边数目鲁棒, 并且超边数目L的增大会抑制公共品博弈中合作行为的涌现. 一定程度上, 本文的研究结果有助于我们更好地理解超图上空间公共品博弈的演化动力学.

     

    The spatial structure and social diversity playing a nontrivial role in the emergence and maintenance of cooperation among selfish individuals have been verified. Their effects on the evolution of cooperation have attracted great attention in recent years. Most of previous evolutionary game dynamics is based on pairwise interactions. However, the interactions often take place within groups of people in many real situations and cannot be described simply by dyads. The dynamics of evolutionary games in systems with higher-order interactions has not yet been explored as deserved. In this paper, we introduce heterogeneous multiplication factors into the spatial public goods game to investigate the cooperative behaviors on the hypergraphs. In addition to the original model in which all groups have the same multiplication factor, three types of heterogeneous multiplication factor distributions including uniform, exponential and power-law distributions are considered. The numerical simulation results show that the increase of the order g of the uniform random hypergraphs is conducive to the emergence and prosperity of the individuals' cooperative behavior no matter what types these distributions belong to. Furthermore, compared with the results of the original spatial public goods games on hypergraphs, the heterogeneous multiplication factors following three different distributions can remarkably promote the evolution of cooperation. In particular, for most of ranges of the average rescaling multiplication factor r_0, the highest cooperation level can be obtained under the power-law distribution, while the uniform distribution leads to the lowest cooperation level. We provide an explanation through investigating the number of cooperators in each group. In addition, to probe into the essence that influences the survival of cooperative behaviors, we study the time series of the fraction of groups with different numbers of cooperators. Besides, we also investigate the influence of the number of hyperlinks on cooperation evolution. We find that the results are robust against the number of hyperlinks L, and the emergence of cooperative behaviors in public goods games on hypergraphs is hindered with the value of L increasing. To some extent, these results are helpful in the better understanding of the evolutionary dynamics of the spatial public goods games on hypergraphs with social diversity.

     

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