On the impossibility of core-selecting auctions

Jacob Goeree and Yuanchuan Lien

No 452, IEW - Working Papers from Institute for Empirical Research in Economics - University of Zurich

Abstract: When goods are substitutes, the Vickrey auction produces efficient, core outcomes that yield competitive seller revenues. In contrast, with complements, the Vickrey outcome, while efficient, is not necessarily in the core and revenue can be very low. Non-core outcomes may be perceived as unfair since there are bidders willing to pay more than the winners' payments. Moreover, non-core outcomes render the auction vulnerable to defections as the seller can attract better offers afterwards. To avoid instabilities of this type, Day and Raghavan (2007) and Day and Milgrom (2007) have suggested to adapt the Vickrey pricing rule. For a simple environment with private information, we show that the resulting auction format yields lower than Vickrey revenues and inefficient outcomes that are on average further from the core than Vickrey outcomes. More generally, we prove that the Vickrey auction is the unique core-selecting auction. Hence, when the Vickrey outcome is not in the core, no Bayesian incentive-compatible core-selecting auction exists. Our results further imply that the competitive equilibrium cannot be implemented when goods are not substitutes. Moreover, even with substitutes, the competitive equilibrium can only be implemented when it coincides with the Vickrey outcome.

Keywords: Core outcomes; Vickrey auction; substitutes; complements; competitive equilibrium; Bayesian implementability (search for similar items in EconPapers)
JEL-codes: D44 (search for similar items in EconPapers)
Date: 2009-11
New Economics Papers: this item is included in nep-cta and nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Journal Article: On the impossibility of core-selecting auctions (2016)
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