Payoff matrix.

Many studies have proposed spatial game theory on network systems. Heterogeneous structures seem to contribute to population dynamics. However, few studies have addressed both dynamical population evolution and network growth events, especially incorporating individual players’ decision-making processes into the model. In this study, we considered a spatial prisoner’s dilemma (SPD) on a random network. In our model, the players were allowed to access the recent past information on themselves and neighboring players. In the “unlikely to happen” scenario, players adopted a strategy that rarely happens, which may have brought some risks to players. Moreover, the players in our model evolved their link with other players by altering their neighborhood when they received a low payoff. As a result, we found that our model spontaneously evolved as an approximate scale-free network around a critical parameter. Interestingly, hub players sometimes decreased their node degree; thus, these players are changeable in our system.