No.626 Funding the Real Deal--Dynamic Moral Hazard with Adverse Selection

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Funding the Real Deal--Dynamic Moral Hazard with Adverse Selection

We study dynamic contracts that incentivize an agent to exert effort to increase the arrival rate of a Poisson arrival (breakthrough), where both the effort cost and the effort level at any time are the agent’s private information. The principal needs to offer a menu of contracts such that each type of agent (with a different effort cost) chooses the corresponding item on the menu. Each item specifies an initial payment, a deadline for the contract, and a payment-upon-arrival process over time. We first fully characterize the optimal menu of contracts when the agent can be one of two types, one good (lower cost) and the other bad. Specifically, the principal should only hire the agent if the revenue of the breakthrough is higher than a threshold. Above this threshold, if the bad agent’s cost is higher than another threshold, the principal should offer a simple linear contract, in which the payment-upon-arrival decreases linearly in time before the deadline. This contract gives the good agent barely sufficient incentive to work, while allowing the bad agent to shirk through the deadline. If the bad agent’s cost is lower than the above threshold, it is worth motivating the bad agent to work using a linear contract while offering the good agent a one-switch contract. The one-switch contract extends the linear contract by allowing the payment-upon-arrival to take a single downward jump at a certain time epoch before the deadline. The optimal contract structure extends to multiple-type cases, in which the one-switch contract becomes a multiple-switch contract. To obtain the entire menu of contracts, one only needs to solve a sequence of linear optimization problems together with a bi-sectional line-search, which is fast to compute and easy to interpret and implement.