Group selection is often cited as an explanation for the survival of altruistic behaviors. The evolutionary dynamic model of altruistic behaviors is established and analyzed. The sufficient and necessary condition for the survival of altruistic behaviors is obtained and proved. Although in a single interaction the altruist is at a disadvantageous position compared with the egoist, altruistic behaviors can survive in the repeated game if the payoff is high enough. This conclusion is useful for the analysis of group mechanism under the framework of evolutionary game theory.
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