Evolution of cooperation with the diversity of cooperation tendencies

Abstract: The complete cooperation and the complete defection are two typical strategies considered in evolutionary games in many previous works. However, in real life, strategies of individuals are full of variety rather than only two complete ones. In this work, the diversity of strategies is introduced into the weak prisoners' dilemma game, which is measured by the diversity of the cooperation tendency. A higher diversity means more cooperation tendencies are provided. The complete cooperation strategy is the full cooperation tendency and the complete defection strategy is without any cooperation tendency. Agents with other cooperation tendencies behave as partial cooperators and as partial defectors simultaneously. The numerical simulation shows that increasing the diversity of the cooperation tendency promotes the cooperation level, not only the number of cooperators but also the average tendency over the whole population, until the diversity reaches its saturated value. Furthermore, our work points out maintaining cooperation is based on the cooperation efficiency approximating to the reward of cooperators and that the cooperation efficiency oscillates and quickly decreases to zero when cooperator clusters cannot resist the invasion of defectors. When the effect of the noise for the Femi update mechanism is considered, a higher diversity of strategies not only improves the cooperation level of the whole population but also supports the survival of more rational agents.