Essays on behavioral mechanism design

Abstract

This collection of essays studies auctions with ambiguity.

In the first chapter, we study the revenue comparison problem of auctions when the seller has a maxmin expected utility preference. The seller holds a set of priors around some reference belief, interpreted as an approximating model of the true probability law or the focal point distribution. We develop a methodology for comparing the revenue performances of auctions: the seller prefers auction X to auction Y if their transfer functions satisfy a weak form of the single-crossing condition. Intuitively, this condition means that a bidder's payment is more negatively associated with the competitor's type in X than in Y. Applying this methodology, we show that when the reference belief is independent and identically distributed (IID) and the bidders are ambiguity neutral, (i) the first-price auction outperforms the second-price and all-pay auctions, and (ii) the second-price and all-pay auctions outperform the war of attrition. Our methodology yields results opposite to those of the Linkage Principle.

The second chapter studies the optimal auction design problem when bidders have maxmin expected utility preferences. Existing literature shows that a full insurance auction is optimal

however, in practice, losing bidders receive no premiums or only partial premiums. Motivated by this observation, we suppose the maximum possible premium that the seller can provide to a bidder is limited by a certain amount. For a given allocation rule, we identify a set of optimal transfer candidates, named the win-lose dependent transfers, with the following property: each type of bidder's transfer conditional on winning or losing is independent of the competitor's type report. Our result reduces the infinite-dimensional optimal transfer problem to a two-dimensional optimization problem. By solving the reduced problem, we find that among efficient mechanisms with no premiums, the first-price auction is optimal. Under a simplifying assumption, the first-price auction with a suitable reserve price remains optimal under the endogenous allocation rule.