The evolution of cooperation in public good game with deposit**Project supported by the National Natural Science Foundation of China (Grant Nos. 71871171, 71871173, and 71701076).

Abstract

The emergence of cooperation still remains a fundamental conundrum in the social and behavior sciences. We introduce a new mechanism, deposit mechanism, into theoretical model to explore how this mechanism promotes cooperation in a well-mixed population. Firstly, we extend the common binary-strategy combination of cooperation and defection in public good game by adding a third strategy, namely, deposit cooperation. The players with deposit cooperation strategy pay a deposit in advance to obtain the benefits of public good at a lower contributions compared with the players with cooperation strategy, when the provision of public good is successful. Then, we explore the evolution of cooperation in the public good game with deposit by means of the replicator dynamics. Theoretical computations and stimulations show that the deposit mechanism can promote cooperation in a well-mixed population, and the numbers of equilibrium point are determined by variables of public good game. On the one hand, when the coexistence of cooperators and defectors is the stable equilibrium point in the evolutionary system, increasing the threshold of public good and adopting the weak altruism way for share benefits can enhance the level of cooperation in the population. On the other hand, if the coexistence of deposit cooperators and defectors is the stable equilibrium point, it is effective to promote the deposit cooperation by lowering the values of discount and deposit, and raising the threshold of public good.