A 2 x 2 game is played repeatedly by two satisficing players. The game considered includes the Prisoner's Dilemma, as well as games of coordination and common interest. Each player has an aspiration at each date, and takes an action. The action is switched at the subsequent period only if the achieved payoff falls below aspirations; the switching probability depends on the shortfall. Aspirations are periodically updated according to payoff experience, but are occasionally subject to trembles. For sufficiently slow updating of aspirations and small tremble probability, it is shown that both players must ultimately cooperate most of the time. Journal of Economic Literature Classification Numbers C72, D83.