Introduction

Practical auction design is often complicated by institutional details and legal or political constraints. For example, using bidder-specific bidding credits or reserve prices may be considered discriminatory and unlawful in some countries making it impossible to implement an optimal auction design. More generally, the use of sizeable reserve prices may cause political stress due to the fear that it slows down technological progress when licenses remain unsold. While constraints of this nature are common and important in practice, mechanism design theory has typically treated them as secondary to incentive constraints.

Recent work by Day and Raghavan (2007), Day and Milgrom (2008), and Day and Cramton (2008) breaks with this tradition and asks how close incentive constraints can be approximated if other (institutional or political) constraints are put first. In particular, these authors have proposed an alternative payment rule to fix some drawbacks of the well-known Vickrey-Clarke-Groves mechanism, or “Vickrey auction” for short. When goods are substitutes the Vickrey auction produces an outcome, i.e. an allocation and payoffs for the seller and bidders, that is in the core. However, when goods are complements, the Vickrey outcome, while efficient, is not necessarily in the core and seller revenue can be very low as a result. Furthermore, non-core outcomes are “unfair” in that there are bidders willing to pay more than the winners’ payments, which makes the auction vulnerable to defections as the seller can attract better offers afterwards. The low revenue, perceived unfairness, and instability of Vickrey outcomes can create legal and political problems, which the alternative payment rule seeks to avoid.

The types of auctions proposed by Day et al. employ a payment rule that insures that outcomes are in the core with respect to reported values, i.e. the final allocation maximizes the total reported value and no coalition of bidders can block the outcome with respect to bidders’ reports. Unless reported values are always truthful, however, it does not imply that core outcomes are produced with respect to bidders’ true preferences.