School of Physics, Nankai University, Tianjin 300071, China.
J Theor Biol. 2011 May 21;277(1):19-26. doi: 10.1016/j.jtbi.2011.02.016. Epub 2011 Feb 25.
In spatial evolutionary games the fitness of each individual is traditionally determined by the payoffs it obtains upon playing the game with its neighbors. Since defection yields the highest individual benefits, the outlook for cooperators is gloomy. While network reciprocity promotes collaborative efforts, chances of averting the impending social decline are slim if the temptation to defect is strong. It is, therefore, of interest to identify viable mechanisms that provide additional support for the evolution of cooperation. Inspired by the fact that the environment may be just as important as inheritance for individual development, we introduce a simple switch that allows a player to either keep its original payoff or use the average payoff of all its neighbors. Depending on which payoff is higher, the influence of either option can be tuned by means of a single parameter. We show that, in general, taking into account the environment promotes cooperation. Yet coveting the fitness of one's neighbors too strongly is not optimal. In fact, cooperation thrives best only if the influence of payoffs obtained in the traditional way is equal to that of the average payoff of the neighborhood. We present results for the prisoner's dilemma and the snowdrift game, for different levels of uncertainty governing the strategy adoption process, and for different neighborhood sizes. Our approach outlines a viable route to increased levels of cooperative behavior in structured populations, but one that requires a thoughtful implementation.
在空间进化博弈中，个体的适应度传统上是由其与邻居玩游戏时获得的收益决定的。由于背叛能带来最高的个体收益，因此合作者的前景黯淡。尽管网络互惠促进了协作，但如果背叛的诱惑很强，那么避免即将到来的社会衰落的机会就很小。因此，确定为合作进化提供额外支持的可行机制很有意义。受环境对个体发展可能与遗传同样重要的事实启发，我们引入了一个简单的开关，允许玩家保持其原始收益或使用其所有邻居的平均收益。根据哪个收益更高，可以通过单个参数来调整每个选项的影响。我们表明，一般来说，考虑环境可以促进合作。然而，过于渴望邻居的适应度并不是最优的。事实上，只有当传统方式获得的收益的影响等于邻居平均收益的影响时，合作才会蓬勃发展。我们针对囚徒困境和雪堆博弈，不同的策略采用过程不确定性水平，以及不同的邻居大小，展示了结果。我们的方法概述了在结构化群体中增加合作行为水平的可行途径，但需要深思熟虑的实施。
