While actors in a population can interact with anyone else freely, social relations significantly influence our inclination towards particular individuals. The consequence of such interactions, however, may also form the intensity of our relations established earlier. These dynamical processes are captured via a coevolutionary model staged in multiplex networks with two distinct layers. In a so-called relationship layer the weights of edges among players may change in time as a consequence of games played in the alternative interaction layer. As an reasonable assumption, bilateral cooperation confirms while mutual defection weakens these weight factors. Importantly, the fitness of a player, which basically determines the success of a strategy imitation, depends not only on the payoff collected from interactions, but also on the individual relationship index calculated from the mentioned weight factors of related edges. Within the framework of weak prisoner's dilemma situation we explore the potential outcomes of the mentioned coevolutionary process where we assume different topologies for relationship layer. We find that higher average degree of the relationship graph is more beneficial to maintain cooperation in regular graphs, but the randomness of links could be a decisive factor in harsh situations. Surprisingly, a stronger coupling between relationship index and fitness discourage the evolution of cooperation by weakening the direct consequence of a strategy change. To complete our study we also monitor how the distribution of relationship index vary and detect a strong relation between its polarization and the general cooperation level.

翻译：尽管群体中的个体可以自由地与任何人互动，但社会关系显著影响我们对特定个体的倾向。然而，这种互动的结果也可能塑造我们先前建立的关系强度。这些动态过程通过一个涉及两个不同层的多重网络协同演化模型来刻画。在所谓的“关系层”中，玩家之间边的权重可能因在另一“互动层”中所进行的博弈结果而随时间变化。作为一个合理假设，双边合作会增强这些权重因子，而相互背叛则会削弱它们。重要的是，玩家的适应性（其基本决定了策略模仿的成功与否）不仅依赖于从互动中获取的收益，还依赖于根据相关边的权重因子计算出的个体关系指数。在弱囚徒困境情景的框架下，我们探索了上述协同演化过程的潜在结果，并对关系层假设了不同的拓扑结构。我们发现，在规则图中，关系图的平均度越高越有利于维持合作，但链接的随机性在严峻情景下可能成为决定性因素。令人惊讶的是，关系指数与适应性之间的强耦合会通过削弱策略变化的直接后果来抑制合作演化。为完善研究，我们还监测了关系指数分布的变化，并检测到其极化程度与总体合作水平之间的强关联。