Dynamic Contract Design in the Presence Of Double Moral Hazard

We consider a stylized incentive management problem over an infinite time horizon, where the principal hires an agent to provide services to customers. Customers request service in one of two ways: either via an online or a traditional, offline, channel. The principal does not observe the offline customers' arrivals, nor does she observe whether the agent exerts (costly) effort that can increase the arrival rate of customers. This creates an opportunity for the agent (i) to divert cash (that is, to under-report the number of offline customers and pocket respective revenues) and also (ii) to shirk (that is, not to exert effort), thus, leading to a novel and so-far-unexplored double moral hazard problem. To address this problem, we formulate a constrained, continuous-time, stochastic optimal control problem and derive an optimal contract with a simple, intuitive structure, that includes a payment scheme and a potential termination time of the agent. We enrich the model to allow the principal to either (i) monitor the agent or (ii) dynamically adjust the prices for the services in both channels. Both tools help the principal to alleviate the double moral hazard problem. We derive respective optimal strategies for using those tools that guarantee highest profits. We show that the worse the agent's past performance is, the more the principal should monitor the agent and the lower the prices should be set. Finally, we demonstrate that sole monitoring of the offline arrivals can, sometimes, make the agent better off, as opposed to the situation when the principal monitors both the offline arrivals and effort, which always makes the agent worse off