The effect of assortativity by degree on emerging cooperation in a 2×2 dilemma game played on an evolutionary network

A series of numerical experiments on 2×2 games using a co-evolutionary model, including both networks and strategies, was performed. A relationship between assortativity by degree of the evolved network and emerging cooperation was investigated. In the Prisoner’s Dilemma (PD) game class, the evolutionary trajectory for a weak dilemma game favors a network with positive assortative coefficient and easily attains a cooperative situation. A game implemented with a stronger dilemma, however, makes the network very heterogeneous, with a negative assortative coefficient required to solve the dilemma situation. This implies that the dilemma strength in the PD significantly affects the direction adopted by the assortative coefficient during evolutionary processes in the co-evolutionary model.