Simultaneously selecting appropriate partners for gaming and strategy adaptation to enhance network reciprocity in the prisoner's dilemma

Network reciprocity is one mechanism for adding social viscosity, which leads to cooperative equilibrium in 2 x 2 prisoner's dilemma games. Previous studies have shown that cooperation can be enhanced by using a skewed, rather than a random, selection of partners for either strategy adaptation or the gaming process. Here we show that combining both processes for selecting a gaming partner and an adaptation partner further enhances cooperation, provided that an appropriate selection rule and parameters are adopted. We also show that this combined model significantly enhances cooperation by reducing the degree of activity in the underlying network; we measure the degree of activity with a quantity called effective degree. More precisely, during the initial evolutionary stage in which the global cooperation fraction declines because initially allocated cooperators becoming defectors, the model shows that weak cooperative clusters perish and only a few strong cooperative clusters survive. This finding is the most important key to attaining significant network reciprocity.