Hybrid learning promotes cooperation in the spatial prisoner's dilemma game

Individuals' strategy updating is an important factor in the spatial prisoner's dilemma game. According to Bandura's social learning theory, adaptive behavior adjustment involves imitating others (i.e. social-learning) and reinforcing the current behaviors based on self-feedback (i.e. self-learning). The existing researches have shown that although social learning and self-learning can promote cooperation under certain conditions, there are some deficiencies in the stability of evolution and the cooperation level. It is, therefore, worthwhile to examine whether hybrid strategy-updating can overcome the deficiencies. In this paper, we propose a hybrid strategy-updating mechanism combining social learning and self-learning. Simulation results show that the proposed hybrid strategy learning mechanism can effectively promote cooperation under appropriate parameter settings. The weight of self-learning and the aspiration of payoff have great impacts on cooperation. We find that at a low aspiration level, higher tendency towards social learning is beneficial to cooperation, while at a high level of aspiration, higher tendency towards self-learning has a significantly positive effect on cooperation. Furthermore, the dynamic mechanism of hybrid learning is explored, revealing that hybrid learning is more conducive to the maintenance of cooperation than social learning and self-learning per se. Finally, through the analysis on the evolutionary stability, we show that the hybrid learning mechanism can prevent the spread of defection when random strategy invasion happens and maintain a high cooperation level.