Comparative Statics of Games Between Relatives

Igal Milchtaich

Theoretical Population Biology 69 (), 203–210


According to Hamilton’s theory of kin selection, species tend to evolve behavior such that each organism appears to be attempting to maximize its inclusive fitness. In particular, two neighbors are likely to help each other if the cost of doing so is less than the benefit multiplied by r, their coefficient of relatedness. Since the latter is less than unity, mutual altruism benefits both neighbors. However, is it theoretically possible that acting so as to maximize the inclusive, rather than personal, fitness may harm both parties. This may occur in strategic symmetric pairwise interactions (more specifically, n × n games), in which the outcome depends on both sides’ actions. In this case, the equilibrium outcome may be less favorable to the interactants’ personal fitness than if each of them acted so as to maximize the latter. This paper shows, however, that such negative effect of relatedness on fitness is incompatible with evolutionary stability. If the symmetric equilibrium strategies are evolutionarily stable, a higher coefficient of relatedness can only entail higher personal fitness for the two neighbors. This suggests that negative comparative statics as above are not likely to occur in nature.


Altruism; Kin selection; Evolutionary game theory; Inclusive fitness ESS; Uninvadability