Cluster evolution in public goods game with fairness mechanism

Defector contributes nothing but gains benefit in public goods game. This phenomenon creates an incentive for free riding and causes inefficient equilibrium in which everyone is defector. However, coexistence of cooperation and defection is pervasive for a large well-mixed population in nature society. Inspired by the fact that humans have strong but also emotional tendencies for fair play, we employ a fairness mechanism with peer punishment to solve the public goods problem of a well-mixed cluster and aim to analyze cluster evolutionary process. The process is divided into three stages. In the first stage called cluster formation, this problem can be effectively solved by same-strategy groups. The second stage is cluster extension, we utilize multiplayer game and prove that increasing fairness factor and decreasing punishment cost are two effective ways to improve cooperation. Finally, we obtain the coexistence of cooperation and defection in the third stage called boom and bust. •The problem in public goods game is solved, and the process of cluster evolution is studied.•Same-strategy group is utilized to obtain full cooperation in small-scale cluster.•Punishment is the emphasis for the formation of cooperation, punishment cost is paid by cooperators evenly.•Fairness mechanism that employs punishment is established.