Abstract
Indirect reciprocity is a key mechanism for the evolution of human cooperation. There are normally two choices in the standard model of indirect reciprocity which works through reputation. Here we introduced the role of costly punishment into the model. The players could have the third choice besides cooperation and defection. The dynamics of cooperation in indirect reciprocity is analyzed under the social norms which depend on the action of the donor and the reputation of the recipient. It is found that those strategies using costly punishment which allow the evolutionary stability of cooperation typically reduce the average payoff of the population and there is only a small parameter region where costly punishment is evolutionary stable and more efficient. The computer simulations based on agent in finite populations are performed and the result is agreement with our theoretical predictions.Keywordscostly punishmentindirect reciprocitydynamicsevolutionary stable strategysocial norm
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