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On the Impossibility of Core-Selecting Auctions


Goeree, Jacob K; Lien, Yuanchuan (2009). On the Impossibility of Core-Selecting Auctions. Working paper series / Institute for Empirical Research in Economics No. 452, 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 environmentnwith private information, we show that the resulting auction format yields lower than Vickrey revenues and inefficient outcomes that are on average further from thencore 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 goodsnare not substitutes. Moreover, even with substitutes, the competitive equilibrium can only be implemented when it coincides with the Vickrey outcome.

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 environmentnwith private information, we show that the resulting auction format yields lower than Vickrey revenues and inefficient outcomes that are on average further from thencore 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 goodsnare not substitutes. Moreover, even with substitutes, the competitive equilibrium can only be implemented when it coincides with the Vickrey outcome.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Institute for Empirical Research in Economics (former)
Dewey Decimal Classification:330 Economics
Language:English
Date:November 2009
Deposited On:29 Nov 2011 20:09
Last Modified:12 Aug 2017 12:47
Series Name:Working paper series / Institute for Empirical Research in Economics
ISSN:1424-0459
Official URL:http://www.econ.uzh.ch/wp.html

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