Robust Automated Mechanism Design

We introduce a new class of mechanisms, robust mechanisms, that is an intermediary between ex-post mechanisms and Bayesian mechanisms. This new class of mechanisms allows the mechanism designer to incorporate imprecise estimates of the distribution over bidder valuations in a way that provides strong guarantees that the mechanism will perform at least as well as ex-post mechanisms, while in many cases performing better. We further extend this class to mechanisms that are with high probability incentive compatible and individually rational, -robust mechanisms. Using techniques from automated mechanism design and robust optimization, we provide an algorithm polynomial in the number of bidder types to design robust and -robust mechanisms. We show that while no mechanism in this class can guarantee better performance than an ex-post mechanism in all cases, experimentally this new class of mechanisms can significantly outperform traditional mechanism design techniques when the mechanism designer has an estimate of the distribution and the bidder’s valuation is correlated with an externally verifiable signal.