Repeated moral hazard with costly self-control

We consider a repeated principal-agent model, where a single agent exhibits problems of self control modelled using Gul and Pesendorfer (2001) type temptation preferences. In such a setting, for a parameterized strength of self-control, we solve for the optimal multi-period contract. Our analysis identifies a new channel of principal and agent interactions, that can be used to provide incentives, this being the reduction of agent's self control costs. In fact, the principal computes (and uses) agent's most tempting item but never finds it optimal to reduce the agent's self-control cost to zero. Presence of this new channel challenges typical results obtained in models with no-temptation on the agent's side. For example, the intrinsic motivation (resulting from costly self-control) can substitute for standard (external) incentives, and hence the moral hazard problem can be mitigated (for sufficiently high temptation parameter). Moreover, the optimal contract calls for a lower deferred part of the bonus (or consumption smoothing) than in the model with no temptations. Under limited commitment, presence of self-control also reduces agent's willingness to break or renegotiate the contract after output realization within some period, and make the optimal contract spot implementable (again for sufficiently high temptation). Impact of self-control on the cost of implementation as well as willingness to safe/borrow is ambiguous, however.