Timing of Effort and Reward: Three-Sided Moral Hazard in a Continuous-Time Model

This paper studies a three-sided moral hazard problem with one agent exerting up-front effort and two agents exerting ongoing effort in a continuous-time model. The agents' efforts jointly affect the probability of survival and thus the expected cash flow of the project. In the optimal contract, the timing of payments reflects the timing of effort: payments for up-front effort precede payments for ongoing effort. Several patterns are possible for the cash allocation between the two agents with ongoing effort. In one case, where the two agents face equally severe moral hazard, they share the cash flow equally at each point of time. In another case, where the two agents have different severities of moral hazard, their payments are sequential. In a more general case, the two agents with ongoing effort first receive the cash flow alternately with an increasing frequency of switches and then divide the cash flow at each point of time. This study provides a framework for understanding a broad set of business-contracting issues. The characteristics suggested in the optimal contract help us analyze the causes of business failure such as the recent debacle of mortgage-backed securities.