Posted Pricing and Prophet Inequalities with Inaccurate Priors

Abstract

In posted pricing, one defines prices for items (or other outcomes), buyers arrive in some order and take their most preferred bundle among the remaining items. Over the last years, our understanding of such mechanisms has improved considerably. The standard assumption is that the mechanism has exact knowledge of probability distribution the buyers' valuations are drawn from. The prices are then set based on this knowledge. We examine to what extent existing results and techniques are robust to inaccurate prior beliefs. That is, the prices are chosen with respect to similar but different probability distributions. We focus on the question of welfare maximization. We consider all standard distance measures on probability distributions, and derive tight bounds on the welfare guarantees that can be derived for all standard techniques in the various metrics.