Contracting in a Continuous-Time Model with Three-Sided Moral Hazard and Cost Synergies

Abstract

We study optimal effort and compensation in a continuous-time model with threesided moral hazard and cost synergies. One agent exerts initial effort to start the project; the other two agents exert ongoing effort to manage it. The project generates cash flow at a fixed rate over its lifespan; cash flow stops if a failure occurs. The three agents’ efforts jointly determine the probability of the project’s survival and thus its expected cash flows. We model cost synergies between the two agents exerting ongoing effort as one’s effort reduces the other’s cost of effort. In the optimal contract, the timing of payments reflects the timing of efforts as well as cost synergies across agents. The agent exerting upfront effort claims all cash flows prior to a predetermined cutoff date, and the two agents exerting ongoing effort divide all subsequent cash flows. Delaying payments motivate these two agents to work hard throughout. Between them, the agent with greater degree of moral hazard and bigger impact on reducing the other agent’s cost claims a larger fraction of the cash flow. Our study sheds light on a broad set of contracting problems, such as compensation plans in startups and profit sharing among business partners.