It is not necessarily a contradiction as long as you accept the existence of two different ways of ranking outcomes: one for desirability and one for decision-making. When a cake is being shared I may want to eat the whole cake alone, but I may still offer you half the cake out of a sense of fairness. For the predictions of game theory it is the decision-making ranking and not the desirability one which enters into payoffs.
If you deny the meaningfulness of talking about different ways of ranking then of course any notion of altruism becomes self-contradictory: "He gains enjoyment by starving himself to feed the poor, that's why he does it." But in practice we distinguish between masochists and saints.
Helping others may help you survive if selfish people are ostracized by others (as seem to happen in human societies) or if a good turn today entitles you to a good turn tomorrow. But the evolutionary theory of altruism is not something I understand very well. My only point was that contrary to what the OP suggests, the formal techniques of game theory such as Nash equilibrium are agnostic with respect to nature of payoffs. And both casual observation and systematic experiments in economics show that many humans act out of a sense of fairness and expect fairness from others even when interacting with strangers.