Promotion of cooperation through co-evolution of networks and strategy in a 2 ×× 2 game

A 2×2 game model implemented by co-evolution of both networks and strategies is established. An existing link between two agents is killed through network adaptation, which then establishes a new link to replace it. Strategy is defined as an offer of “cooperation” (C) or “defection” (D) by an agent. Both networks and strategies are synchronously renovated in each simulation time step. After killing the link with the most disadvantageous neighbor, we consider network adaptations that involve rewiring to (1) a randomly selected agent, (2) a proportionally selected agent (through a roulette selection process based on the degrees of respective agents), (3) an agent randomly selected among a set of neighbors of the neighbors, excluding the most disadvantageous neighbor. Several numerical experiments considering various 2×2 game classes, including Prisoner’s Dilemma (PD), Chicken, Leader, and Hero, reveal that the proposed co-evolution mechanism can solve dilemmas in the PD game class. The result of solving a dilemma is the development of mutual-cooperation reciprocity (RR reciprocity), which arises through the emergence of several cooperative hub agents, which have many links in a heterogeneous and assortative social network. However, the co-evolution mechanism seems counterproductive in the case of the Leader and Hero game classes, where alternating reciprocity (ST   reciprocity) is more demanding. It is also suggested that the assortative and cluster coefficients of a network affect the emergence of cooperation for RR reciprocity.