Technical Note—Dynamic Mechanism Design with Capacity Constraint

We study a project assignment problem, where a principal needs to assign multiple projects to an agent. The agent is privately informed about the cost, which could be high or low. The agent’s type evolves stochastically over time. We fully characterize the optimal mechanism via a sequence of deadlines and show that the presence of the capacity constraint reduces the principal’s payoff and delays the assignment of projects. In particular, as the number of projects increases, the limit optimal contract may be strictly bounded away from the optimal contract when there are infinitely many projects, and the principal’s payoff may be strictly below that in the setting without the capacity constraint.

Funding: This work was supported by the National Natural Science Foundation of China [Grant 72122023].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2449.