Game of full siblings in Mendelian populations

We adapt the concept of evolutionary stability to familial selection when a game theoretic conflicts between siblings determines the survival rate of each sibling in monogamous, exogamous families in a diploid, panmictic population. Similarly to the classical evolutionary game theory, the static condition of evolutionary stability of mixed Nash equilibrium implies the local stability of the genotype dynamics, in spite of that the mating table based genotype dynamics is not a replicator dynamics. We apply our general result to the case where a matrix game determines the survival rate of siblings. In our numerical studies we consider the prisoners dilemma between siblings, when the cooperator and defector behaviour are unequally determined by a recessive-dominant allele pair at an autosomal locus. When the prisoners dilemma game is strict (cf. iterated one) and the cooperator phenotype is recessive resp. dominant, then the cooperator and defector phenotypes are the unique stable phenotypes, respectively. When the prisoners dilemma game is not strict, both phenotypes coexist, independently of the genotype-phenotype mapping. However, the frequencies of the phenotypes are different according to which phenotype is dominant.