Cooperation evolves by the payoff-difference-based probabilistic reward

Abstract

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. Graphic abstract

Cooperation without punishment

“…The literature on cooperation explores various mechanisms that do not rely on punishment. These include cognitive factors such as intuition and deliberation 48 – 50 , as well as psychological factors, such as imitation of emotions 51 , 52 , positive interactions 53 , 54 , and rewards 55 – 58 . Other mechanisms include the coevolution of norms 59 , 60 , the coevolution of costs and benefits 61 , and opting out from the public good game altogether 62 – 64 .…”

Costly incentives design from an institutional perspective: cooperation, sustainability and affluence

“…A few works have considered minimizing the cost of incentive enforcement from the perspective of optimization, and managed to design cost-effective reward or punishment [38][39][40][41][42] for an external third-party (or external decision-maker [26]). In these studies, the third party is composed of agents that do not belong to the system, and the income of such an external third party was not considered.…”