Optimal multi-unit allocation with costly verification

A principal has n homogeneous objects to allocate to \(I> n\) agents. The principal can allocate at most one good to an agent, and each agent values the good. Agents have private information about the principal’s payoff of allocating the goods. There are no monetary transfers, but the principal may check any agent’s value at a cost. In this setting, we propose a direct mechanism, called the n-ascending mechanism, which balances the benefit of efficient allocation and the cost of checking agents. While such a mechanism itself is not obviously strategy-proof, we show that its outcome is easily implementable by an extensive game which has an equilibrium in obviously dominant strategies. When \(n = 2,\) we show that the 2-ascending mechanism is essentially the unique optimal mechanism that maximizes the principal’s expected net payoff.