Scale-Free Relationships Facilitate Cooperation in Spatial Games with Sequential Strategy

Recently, the area of study of spatial game continuously has extended, and researchers have especially presented a lot of works of coevolutionary mechanism. We have recognized coevolutionary mechanism as one of the factors for the promotion of cooperation like five rules by Nowak. However, those studies still deal with the optimal response (best decision). The best decision is persuasive in most cases, but does not apply to all situations in the real world. Contemplating that question, researchers have presented some works discussing not only the best decision but also the second-best decision. Those studies compare the results between the best and the second-best, and also state the applicability of the second-best decision. This study, considering that trend, has extended the match between two groups to spatial game with the second-best decision. This extended model expresses relationships of groups as a spatial network, and every group matches other groups of relationships. Then, we examine how mutual cooperation changes in each case where either we add probabilistic perturbation to relationships or ties form various types of the structure. As a result, unlike most results utilizing the best decision, probabilistic perturbation does not induce any change. On the other hand, when ties are the scale-free structure, mutual cooperation is enhanced like the case of the best decision. When we probe the evolution of strategies in that case, groups with many ties play a role for leading the direction of decision as a whole. This role appears without explicit assignment. In the discussion, we also state that the presented model has an analogy to the real situation, collusive tendering.