On the evolution of altruism

We demonstrate how altruism can flourish in a population of nonaltruists. We assume that each individual plays a one-shot prisoner's dilemma game with his or her sibling and that the probability than an individual survives to reproduce is proportional to his or her payoff in this game. We model the formation of couples and the rule of imitation of parents and of nonparents. We then ask what happens to the proportion of altruists in the population. We specify a case where the unique and stable equilibrium is one in which the entire population will consist of altruists.