Exploring Efficient Reward Strategies to Encourage Large-Scale Cooperation Among Boundedly Rational Players with the Risk and Impact of the Public Good

In a public goods game, while cooperators need to make contributions, defectors can take a free ride after the realization of the public good. The Nash equilibrium in this game is simply zero contribution from all the players. A conventional approach to encourage cooperation and achieve the public good is using rewards to compensate the difference between the cooperators’ and the defectors’ payoffs. However, the public good may not be realized due to the uncertainty in the game, and the conventional way could underestimate the required rewards to achieve the public good. On the other hand, public good did realize in human history when people cannot survive from a natural disaster, such as a big flood, without cooperating to build a solid embankment, and most of them are willing to choose cooperation without rewards. The realization of the public good leads to the reduction of the defection cost and the contribution, which has a potential to encourage the players’ cooperation. Then the conventional method may overestimate the necessary rewards to realize the public good. In this paper, a public goods game is employed to model the interaction among boundedly rational players with the rewards for large-scale cooperation, and a behavioral game-theoretic approach is developed to describe their decision making processes with the consideration of the risk and impact of public good in the game. It turns out that the conventional rewards to achieve the large-scale cooperation can be reduced for a favorable group of the players.