Optimal Sequential Assignment with Capacity Constrained Verification

A principal seeks to allocate $k$ identical objects among n sequentially arriving, impatient agents. Each agent privately observes her valuation, and the principal's payoff from allocating an object depends on the recipient's valuation. The principal can perfectly verify the valuation of at most $m$ agents, where $m < k$, and commits to a mechanism before any agent arrives. We characterize the class of optimal mechanisms. Our main result establishes that, in states where the number of remaining objects exceeds the number of available verification checks, the optimal mechanism may involve probabilistic verification.