Mechanism design with belief-dependent preferences

This paper studies mechanism design when agents have belief-dependent preferences, in that utilities depend on the agents' hierarchical posterior beliefs about types. For instance, agents may be subject to temptation, shame, image concerns, or privacy concerns. In this setting, the textbook revelation principle does not hold, since mechanisms can provide agents with information that affects posterior beliefs. This paper uses a psychological game framework suited for mechanism design, and provides a novel version of the revelation principle for belief-dependent preferences. The new revelation principle makes use of extended direct mechanisms that map each reported type into material outcomes and private suggestions of what posterior beliefs the agents should have. The paper shows that it suffices to use extended direct mechanisms that satisfy three conditions: Bayesian incentive compatibility, individual rationality, and a new condition called believability. The new revelation principle is used to find revenue-maximizing auctions when bidders have different types of image concerns. Moreover, it provides an alternate tool—distinct from Myerson's communication revelation principle—to study mechanism design with after-games.