We offer a game-theoretic proof of Hamilton's rule for the spread of altruism. For a simple case of siblings, we show that the rule can be derived as the outcome of a one-shot prisoner's dilemma game between siblings.

We demonstrate how altruism can surge in a population of nonaltruists. We assume that each individual plays a one-shot prisoner's dilemma game with his or her sibling, or with a stranger, and that the probability that an individual survives to reproduce is proportional to his or her payoff in...