We study dynamic contracts that incentivize an agent to exert effort to increase the arrival rate of a Poisson breakthrough, where both the effort cost and the effort level at any time are the agent’s private information. Optimally, the principal offers a menu of contracts, each tailored to an agent type (with a different effort cost), specifying an initial payment, a contract deadline, and a payment-upon-arrival process over time. We first fully characterize the optimal contract menu in a two-type setting, where the agent is either a good (low-cost) or bad (high-cost) type. Specifically, the principal should hire the agent only if the breakthrough revenue exceeds a threshold. Above this threshold, if the bad agent’s cost is higher than another threshold, it is optimal to motivate only the good type to exert effort. The principal offers the good type a simple linear contract in which the payment-upon-arrival declines linearly over time until the deadline, whereas the bad type receives an initial payment and leaves immediately. The linear contract provides just enough incentive for the good agent to work. If the bad agent’s cost falls below the threshold, it becomes optimal to also motivate the bad agent to work using a linear contract, whereas offering the good agent a one-switch contract. The one-switch contract extends the linear form by allowing the payment-upon-arrival to take a single downward jump at a specific time 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 bisectional line-search, which is fast to compute and easy to interpret and implement. Funding: F. Tian acknowledges funding support from Hong Kong Research Grants Council General Research Fund Grants 17502023 and 17503424. Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1156 .
Tian et al. (Thu,) studied this question.