Impact of generalized benefit functions on the evolution of cooperation in spatial public goods games with continuous strategies
Impact of generalized benefit functions on the evolution of cooperation in spatial public goods games with continuous strategies
复制标题
广义收益函数对连续策略空间公共物品博弈合作演化的影响
DOI：
10.1103/physreve.85.066133
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发表时间：
2012-06-29
影响因子：
2.4
通讯作者：
Wang, Long
中科院分区：
文献类型：
--
作者：
Chen, Xiaojie;Szolnoki, Attila;Wang, Long
合作和背叛可以被认为是对社会困境的两种极端反应。然而现实却远没有那么明确。在这两个极端之间存在着一段矛盾选择的区间，理论上可以通过定义每个参与者对公共池的贡献程度的连续策略来捕获该区间。如果从单位区间选择策略，其中 0 对应于纯粹的背叛，1 对应于最大贡献，那么问题是，如果演化由不同的收益函数引导，那么个人投资对公共池的特征水平是多少。在这里，我们将陡度和阈值视为定义一系列广义收益函数的两个参数，并且我们表明，在结构化总体中，存在两者的中间值，在该值处集体贡献最大。然而，随着合作成本效益比的增加，特征阈值降低，而相应的陡度增加。如果使用更复杂的 sigmoid 函数，我们的观察结果仍然有效，从而强化了仔细调整收益对于高水平公共合作的重要性。
Cooperation and defection may be considered to be two extreme responses to a social dilemma. Yet the reality is much less clear-cut. Between the two extremes lies an interval of ambivalent choices, which may be captured theoretically by means of continuous strategies defining the extent of the contributions of each individual player to the common pool. If strategies are chosen from the unit interval, where 0 corresponds to pure defection and 1 corresponds to the maximal contribution, the question is what is the characteristic level of individual investments to the common pool that emerges if the evolution is guided by different benefit functions. Here we consider the steepness and the threshold as two parameters defining an array of generalized benefit functions, and we show that in a structured population there exist intermediate values of both at which the collective contributions are maximal. However, as the cost-to-benefit ratio of cooperation increases, the characteristic threshold decreases while the corresponding steepness increases. Our observations remain valid if more complex sigmoid functions are used, thus reenforcing the importance of carefully adjusted benefits for high levels of public cooperation.