Open AccessOn the impossibility of core‐selecting auctions
Author(s) -
Goeree Jacob K.,
Lien Yuanchuan
Publication year - 2016
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te1198
Subject(s) - outcome (game theory) , vickrey auction , core (optical fiber) , vickrey–clarke–groves auction , economics , microeconomics , generalized second price auction , mathematical economics , common value auction , english auction , bidding , impossibility , revenue , auction theory , proxy bid , computer science , finance , telecommunications , political science , law
When goods are substitutes, the Vickrey outcome is in the core and yields competitive seller revenue. In contrast, with complements, the Vickrey outcome is efficient but not necessarily in the core and revenue can be 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 afterward. To avoid instabilities of this type, Day and Raghavan (2007), Day and Milgrom (2008), and Day and Cramton (2012) have suggested adapting the Vickrey pricing rule so that outcomes are in the core with respect to bidders' reported values. If truthful bidding were an equilibrium of the resulting auction, then the outcome would also be in the core with respect to bidders' true values. We show, however, that when the equilibrium outcome of any auction is in the core, it is equivalent to the Vickrey outcome. In other words, if the Vickrey outcome is not in the core, no core‐selecting auction exists. Our results further imply that the competitive equilibrium outcome, which always exists when goods are substitutes, can only be implemented when it coincides with the Vickrey outcome. Finally, for a simple environment, we show that compared to Vickrey prices, the adapted pricing rule yields lower expected efficiency and revenue as well as outcomes that are on average further from the core.