Evolutionary stability of discriminating behaviors with the presence of kin cheaters

Discriminating altruism, particularly kin altruism, is a fundamental mechanism of cooperation in nature. Altruistic behavior is not favored by evolution in the circumstances where there are "kin cheaters" that cannot be effectively identified. Using evolutionary iterated prisoner's dilemma, we deduce the condition for discriminating strategies to be evolutionarily stable and show that the competition between groups of different discriminating strategies restrains the percentage of kin cheaters. A discriminating strategy (DS) manages to cooperate with kin members and defect against non-kins by using an identification mechanism that includes a predetermined sequence of cooperation and defection. The opponent is identified as a kin member if it plays the same sequence. Otherwise, it is identified as non-kin, and defection will be triggered. Once the DS forms the majority of the population, any strategy that does not play the same sequence of moves will be expelled. We find that the competition between a variety of discriminating strategies favors a stable rate of cooperation and a low frequency of kin cheaters.