Chen Xiaojie, Szolnoki Attila, Perc Matjaž, Wang Long
Evolution and Ecology Program, International Institute for Applied Systems Analysis, Schlossplatz 1, A-2361 Laxenburg, Austria.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066133. doi: 10.1103/PhysRevE.85.066133. Epub 2012 Jun 29.
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.
合作与背叛可被视为对社会困境的两种极端反应。然而现实要模糊得多。在这两个极端之间存在一个矛盾选择区间，理论上可以通过定义每个个体参与者对公共资源贡献程度的连续策略来捕捉。如果策略是从单位区间中选取，其中0对应纯粹背叛，1对应最大贡献，那么问题是如果进化由不同的收益函数引导，个体对公共资源的特征性投资水平是什么。在这里，我们将陡峭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种群中，两者都存在中间值，此时集体贡献最大。然而，随着合作的成本效益比增加，特征阈值降低而相应的陡峭度增加。如果使用更复杂的S形函数，我们的观察结果仍然有效，从而进一步强调了为高水平公共合作精心调整收益的重要性。
