The effects of heterogeneous confidence on cooperation in spatial prisoner's dilemma game

Confidence, which characterizes the feeling when people evaluate something, could influence their choices or behaviors significantly. Under the framework of evolutionary game theory, Szolnoki and Chen (Phys. Rev. E, 98 (2018) 022309) found that, both underconfident and overconfident individuals can promote cooperation in the population. In their work, underconfident and overconfident individuals are both assumed to have homogeneous confidence levels and the confidence levels remain unchanged during the whole evolutionary process. As a direct extension, in this work, we treat confidence level as an attribute of the individuals and assign each one a confidence level, which may be static or time-varied. The effects of heterogeneous confidence on cooperation in evolutionary games are investigated and two different cases are considered. For the static case, we assume that individuals' confidence levels are drawn from a uniform distribution in a certain interval. Whereas, for the time-varied case, the confidence levels of individuals can coevolve with the strategies. By numerical simulation, we find that the static heterogeneous confidence can enhance cooperation when the parameters of distribution satisfy certain conditions. Some analytic explanations based on the observations of strategy configurations among the population are provided. Furthermore, when individuals' confidence levels are allowed to coevolve with their strategies during the evolutionary dynamics, cooperation could be significantly improved. We also find that there exists an optimal increment for the confidence level which leads to the highest cooperation level.