This paper explores the evolutionary foundations of altruism among siblings and extends the biologists' kin-selection theory to a richer class of games between relatives. It shows that a population will resist invasion by dominant mutant genes if individuals maximize a "semi-Kantian" utility function in games with their siblings. It is shown that a population that resists invasion by dominant mutants may be invaded by recessive mutants. Conditions are found under which a population resists invasion by dominant and also by recessive mutants.