Asymmetrical influence of population is ubiquitous in human and animal societies. Based on this fact, we construct a setup of asymmetric influence of structured population, which is often put with the combination mechanism of tolerance and punishment when the dispute of unfair outcome happens, to investigate the evolution of cooperation. In detail, the structured populations are classified into two types: A-type players (strong players) and B-type players (weak players). A-type players are capable to decide whether or not to lower the fitness of B-type neighbors with punitive action due to the tolerance limits. This action affects the behavior of B-type neighbors in the evolutionary game. Based on our simulations, it is noted that the mechanism of punishment combining with tolerance in an asymmetrical environment can promote the evolution of cooperation. Furthermore, the lower threshold of tolerance with the looser punishment, the higher the level of cooperation; and the higher degree of tolerance with the stricter punishment will maintain the survival of cooperators. It is also worth mentioning that if A-type population is the key minority impacting the majority of B-type, they can favor affecting and further promoting the evolution of cooperation in the evolutionary game.

中文翻译：

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不对称影响促进空间社会困境中的合作

人口的不对称影响在人类和动物社会中普遍存在。基于这一事实，我们构建了一个结构化群体的不对称影响的设置，当发生不公平结果的争议时，该设置通常与容忍和惩罚相结合的机制来研究合作的演变。具体而言，结构化人群分为两类：A型玩家（强玩家）和B型玩家（弱玩家）。由于容忍限制，A 型玩家能够决定是否通过惩罚行动降低 B 型邻居的适应度。这个动作会影响进化博弈中 B 型邻居的行为。根据我们的模拟，值得注意的是，在不对称环境中惩罚与容忍相结合的机制可以促进合作的演进。此外，容忍门槛越低，惩罚越宽松，合作水平越高；更高的容忍度和更严厉的惩罚将维持合作者的生存。还值得一提的是，如果 A 型种群是影响大多数 B 型种群的关键少数群体，他们可以在进化博弈中有利于影响和进一步促进合作的进化。