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).

Pdf.

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.

Bidding à la Hicks: Which scoring rule is optimal for infrastructure procurement auctions?

Infrastructure projects are notoriously unpredictable. When governments auction these projects to private firms, who should bear these risks? Which auction format should the government use? How can they employ taxpayer money efficiently?

Scaling auctions (also known as unit-price auctions) are procurement mechanisms where firms bid unit prices for each task in a project, with the lowest weighted score winning. The winning firm is paid based on actual quantities used during construction allowing firms to transfer some quantity risk to the government.

In our recent paper, "Scaling Auctions in Procurement Settings with Risk-Averse Sellers," Allan Hernandez and I investigate how different scoring rules distribute financial risk between governments and construction firms. We show that bidding behavior in scaling auctions takes a simple form: bids follow an auxiliary Hicksian demand in which scoring weights act as prices, explaining the "skewed bidding" phenomenon often observed in empirical studies. Our most main finding is that the optimal scoring rule uses weights proportional to expected quantities—exactly what governments have been using.

Through this framework, we show that scaling auctions (where firms bid unit prices) outperform cash auctions (where firms bid fixed amounts) when marginal costs are sufficiently high relative to fixed costs. We also identify a hybrid auction format that outperforms both formats by allowing firms to optimally hedge against project risks.

Our findings provide clear guidance to government procurement agencies on when to use each auction format based on project characteristics. One the one hand we show that governments have used the optimal scoring rule. On the other hand though, we challenge the current practice of prohibiting bid skewing.

Working paper: Pdf

Abstract: We study scaling auctions in procurement settings with risk-averse sellers, showing that bidding behavior follows an auxiliary Hicksian demand in which scoring weights act as prices. As a result, changes in weights induce a pure substitution effect, providing a rationale for skewed bidding behavior observed in empirical studies. By using the Hicksian properties, we characterize the optimal scaling auction and show that it outperforms cash auctions if and only if marginal costs are sufficiently high. Additionally, we identify a hybrid auction format that outperforms both scaling and cash auctions.