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There has been an urgent challenge for environmental protection due to issues like population increase, climate change, and pollution. To address this challenge, sustained human cooperation is critical. However, how cooperation in human beings evolves is one of the 125 most challenging scientific questions, as announced by Science in its 125th anniversary. In this paper, we contribute to answering this question by building an economic game model based on indirect reciprocity and altruism behavior. In our model, there are three types of participants: cooperator, defector, and discriminator. In every round of the game, the cooperator chooses cooperation, the defector chooses non-cooperation, and the choice of the discriminator depends on the choice of his partner in the last round. Our analysis and main result shows that there is no stable evolution equilibrium in this game, which implies that the proportions of different types of players will keep changing instead of reaching a stable equilibrium. In other words, there is no guarantee that cooperation will be dominant in this game. An implication of this result is that to achieve cooperation and protect the environment more effectively, cooperators and discriminators in our society should be provided with incentives.

An Economic Model of Human Cooperation Based on Indirect Reciprocity and Its Implication on Environmental Protection