On incentives, temptation and self-control

• I consider a principal–agent model with a tempted agent.
• The incentive compatibility constraint is not necessarily binding at the optimal solution.
• The solution to the relaxed problem (without the incentive compatibility constraint) provides a variable pay (even for the separable utility case).
• I show monotone comparative statics results of the optimal contract with the strength of temptation.

We consider a principal–agent model, where a single agent exhibits problems of self control modeled using Gul and Pesendorfer (2001) type temptation preferences. For a general class of preferences, we characterize the optimal contract in such a setting using standard Grossman and Hart (1983) techniques. Our analysis shows that the incentive compatibility constraint is not necessarily binding at the optimal solution. As a result, the solution to the relaxed problem (without the incentive compatibility constraint) provides a variable pay, which contrasts with the standard results for the separable utility case. These observations result from the fact that in our setting the principal trade-offs incentives and insurance, but also reduction of self control cost for the agent. Our results shed some light on the justification of randomized contracts (see Holmstrom, 1979), the literature on behavioral contracts, but also show that in the presence of strong self-control problems moral hazard cost can be mitigated.