Zhang Hui, Gao Meng, Wang Wenting, Liu Zhiguang
Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi׳an, Shaanxi 710027, China.
Yantai Institute of Coastal Zone Research, CAS, Yantai 264003, China.
J Theor Biol. 2014 Oct 7;358:122-31. doi: 10.1016/j.jtbi.2014.05.038. Epub 2014 Jun 5.
A game-theoretical model is constructed to capture the effect of external constraint on the evolution of cooperation. External constraint describes the case where individuals are forced to cooperate with a given probability in a society. Mathematical analyses are conducted via pair approximation and diffusion approximation methods. The results show that the condition for cooperation to be favored on graphs with constraint is b¯/c¯>k/A¯ (A¯=1+kp/(1-p)), where b¯ and c¯ represent the altruistic benefit and cost, respectively, k is the average degree of the graph and p is the probability of compulsory cooperation by external enforcement. Moreover, numerical simulations are also performed on a repeated game with three strategies, always defect (ALLD), tit-for-tat (TFT) and always cooperate (ALLC). These simulations demonstrate that a slight enforcement of ALLC can only promote cooperation when there is weak network reciprocity, while the catalyst effect of TFT on cooperation is verified. In addition, the interesting phenomenon of stable coexistence of the three strategies can be observed. Our model can represent evolutionary dynamics on a network structure which is disturbed by a specified external constraint.
构建了一个博弈论模型来捕捉外部约束对合作演化的影响。外部约束描述了个体在社会中被迫以给定概率进行合作的情况。通过对近似和扩散近似方法进行数学分析。结果表明，在有约束的图上有利于合作的条件是b¯/c¯>k/A¯（A¯=1+kp/(1-p)），其中b¯和c¯分别代表利他收益和成本，k是图的平均度，p是外部强制下强制合作的概率。此外，还对具有三种策略的重复博弈进行了数值模拟，即总是背叛（ALLD）、针锋相对（TFT）和总是合作（ALLC）。这些模拟表明，当网络互惠性较弱时，对ALLC的轻微强制只能促进合作，而TFT对合作的催化作用得到了验证。此外，可以观察到三种策略稳定共存的有趣现象。我们的模型可以表示在受到特定外部约束干扰的网络结构上的进化动力学。
