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.

I. Introduction

Cooperation is not uncommon in even the most aggressive species, and numerous costly and fitness-reducing behaviors remain stable in evolution. Among the many explanations of cooperation in nature, kin altruism is by far the most incontrovertible as evidenced by the significant body of scientific literature [1]–[4]. Hamilton's rule depicts the condition of kin altruism by , where is the relatedness between two individuals, and are the benefit to the recipient and the cost to the altruist, respectively [1], [2]. Even though the altruist may reduce their own fitness, the behavior increases the fitness of their relatives with which they share the same gene. As altruistic behavior has developed among the individuals that may share the same gene, the species as a whole receives significantly higher fitness in evolution than that it would have been if there was no kin altruism.