What is the best auction format when bidders wish to flaunt?
Traditional economic models miss a crucial piece of human behavior - our deep desire to shape how others perceive us. Whether it's art collectors wanting to appear cultured or donors seeking social recognition, these "image concerns" fundamentally change the way we bid in auctions.
In my recent paper, "Mechanism Design with Belief-Dependent Preferences," I explore how these image concerns impact the optimal design of auctions. I establish a novel version of the revelation principle for environments with belief-dependent preferences, showing that all equilibrium outcomes can be achieved through truth-telling in a class of "extended direct mechanisms."
This framework allows us to characterize revenue-maximizing auctions when bidders care about others' perceptions. While optimal allocation rules may mirror standard settings, the optimal information disclosure policy of the auction depends critically on the specific type of image concern.
Published in the Journal of Economic Theory (2024).
Abstract 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.
