On the Futility of Dynamics in Robust Mechanism Design

We consider a principal who repeatedly interacts with a strategic agent holding private information. In each round, the agent observes an idiosyncratic shock drawn independently and identically from a distribution known to the agent but not to the principal. The utilities of the principal and the agent are determined by the values of the shock and outcomes that are chosen by the principal based on reports made by the agent. When the principal commits to a dynamic mechanism, the agent best-responds to maximize his aggregate utility over the whole time horizon. The principal’s goal is to design a dynamic mechanism to minimize his worst-case regret, that is, the largest difference possible between the aggregate utility he could obtain if he knew the agent’s distribution and the actual aggregate utility he obtains. We identify a broad class of games in which the principal’s optimal mechanism is static without any meaningful dynamics. The optimal dynamic mechanism, if it exists, simply repeats an optimal mechanism for a single-round problem in each round. The minimax regret is the number of rounds times the minimax regret in the single-round problem. The class of games includes repeated selling of identical copies of a single good or multiple goods, repeated principal-agent relationships with hidden information, and repeated allocation of a resource without money. Outside this class of games, we construct examples in which a dynamic mechanism provably outperforms any static mechanism.