The static or dynamic notions of equilibrium proposed in game theory can be justified from two perspectives. From an educational point of view, equilibrium results from the sole reasoning of hyperintelligent players who have a common knowledge of the structure of the game and their respective rationalities. If the rationalizable equilibrium or the correlated equilibrium are easily justified, the Nash equilibrium is obtained only under very drastic conditions; as for the perfect equilibrium, its justification is very sensitive to the hypotheses made. From the evolutionist point of view, balances result from the convergence of a process of learning or evolution of players in limited rationality, but observing the past course of the game. The Nash equilibrium, at least in pure strategies, is often obtained as an asymptotic state and some of its refinements can even be selected; the perfect balance is also justified under very extensive conditions