Dual-process theories view decisions as the result of the interaction of two qualitatively different types of processes, automatic/impulsive and controlled/deliberative. This paper considers a model of self-control where each decision can be taken by either an automatic process or a deliberative one. In line with recent evidence from psychology, effortful self-control (willpower) is modeled as a limited resource, i.e. exercising self-control for an initial decision limits the amount of self-control available for persevering later. Automatic decisions follow a reinforcement-based process, while controlled ones are utility-maximizing. A "personal evolution" approach shows that agents might fall into self-control traps: for instance, although exercising full self-control might be efficient, decision makers might be caught in a "personal optimum" where no self-control is exercised. Reciprocally, agents might also fall prey to excessive self-control, where they waste willpower in initial decisions only to give in to temptation later.
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