Cooperation evolves by the payoff-difference-based probabilistic reward

In the previous studies, the author proposes the payoff-difference-based probabilistic peer-punishment that the probability of punishing a defector increases as the difference of payoff between a player and a defector increases and shows that the proposed peer-punishment effectively increases the number of cooperators and the average payoff of all players. On the other hand, reward as well as punishment is considered to be a mechanism promoting cooperation, and many studies have discussed the effect of reward in the public goods game, a multiplayer version of the prisoner’s dilemma game. Based on the discussion of those existing studies, this study introduces the payoff-difference-based probabilistic reward that the probability of rewarding a cooperator increases as the difference of payoff between a player and a cooperator increases. The author utilizes the framework of the spatial prisoner’s dilemma game of the previous study and shows that the reward of this study realizes the evolution of cooperation except some cases