Self-Control, Moderate Consumption and Craving

We analyse the consumption strategy of a dynamically inconsistent individual for goods that provide an immediate benefit and a delayed cost. The agent has incomplete information on the cost inherent to each unit of consumption and partially learns this value anytime he consumes. We show that, by fear of overconsuming indefinitely, the agent may (optimally) decide to abstain after some periods, even in cases where moderate consumption always dominates abstention. This provides a rationale for why dieters, former smokers, or gamblers stick to strict personal rules of behaviour, such as total abstention, without invoking standard addiction arguments. We also study how urges modify the strategy of the agent and analyse some policy implications. Last, applications of this theory to other issues such as self-knowledge, willpower and habit formation are discussed.