Essays on Dynamic Incentives

This thesis consists of three essays on dynamic contracts or games with incomplete information. In Chapter 1, I study concealing losses in dynamic relationships. I investigate a continuous-time reputation game, where an agent privately observes a Poisson process of losses and chooses whether to disclose them to the principal or to conceal them. By disclosing a loss, the agent passes on the consequences to the principal, which is an observable event. By concealing a loss, the agent bears the consequences himself, and the principal is unaware of the occurrence. The agent's type is private and uncertain: he is either strategic or honest. An honest agent faces a lower rate of losses and always discloses them. Both the principal and the agent enjoy a flow of benefits from the relationship while it is active. The principal, however, may unilaterally end the relationship at any time, and she prefers to maintain a relationship only with the low-frequency (honest) type. She learns about the agent's type through the pattern of disclosed losses. I characterize a class of equilibria with an intuitive structure consisting of a milking phase at high reputation and a building phase at low reputation. In the milking phase, every loss is passed through and is tolerated by the principal. In the building phase, the strategic type of agent probabilistically passes through losses and the principal randomly terminates the relationship when she incurs one. Applications include filing insurance claims, employees who make costly mistakes and friends or colleagues who ask for favors.

In Chapter 2, I employ novel methods to investigate optimal project management in a setting plagued by unavoidable setbacks. The contractor can cover up delays from shirking either by making false claims of setbacks or by postponing the reports of real ones. The sponsor induces work and honest reporting via a soft deadline and a reward for completion. Late-stage setbacks trigger randomization between cancellation and extension. Thus the project may run far beyond its initial schedule, generating arbitrarily large overruns, and yet be canceled. Absent commitment to randomize, the sponsor grants the contractor more time to complete the project.

In Chapter 3, I study the optimal incentive scheme for a long-term project with both moral hazard and adverse selection. The moral hazard issue is due to the fact that the agent's effort, which increases the arrival rate of a Poisson process, is not observable by the principal. In addition, the agent's effort cost, which needs to be reimbursed by the principal, is also the agent's private information. This gives rise to the adverse selection problem. The principal needs to design the optimal menu of contracts, each of which is chosen by the agent with a specific effort cost. I fully characterize the optimal menu in the case of two types of agents. Specifically, the agent with a lower cost is offered a probation contract, which confirms the agent's type if there is an arrival during a probation period; the agent with the higher cost is offered a sign-on-bonus contract with an immediate direct initial payment. I then explore the more general case with continuous types of agents. In particular, I provide an easy-to-compute upper bound on the principal's utility. The upper bound computation also yields a feasible menu of probation and sign-on-bonus contracts, and the corresponding lower bound it generates. I further provide a condition which can be used to verify whether the upper and lower bounds coincide, implying the optimality of our feasible menu of contracts. Numerical studies confirm that the verification condition almost always holds for commonly used probability distributions of the effort cost.