The two-person Prisoner's Dilemma (PD) game is decomposed in three different ways. The games differ with respect to positive and negative outcomes, whether they are played simultaneously or sequentially and whether one or the other person is allowed to play the sequential game first. The observed strategies of 52 participants playing these games in a computer experiment are explained by the values of the payoffs, the expectations regarding the other person's moves and by personal information. It appears that a subjective expected utility model can be used to test different psychological models of choice. A model assuming segregated evaluation of the payoffs in the sequential games gives a better explanation of the choices than a model assuming integration of payoffs. This implies some rules for giving rewards for behavior in the social dilemma situations concerned.