auction with some tie-breaking would rule still be the unique feasible auction
form.
Our model provides support to the English auction in the general class of auc-
tion mechanisms. Many studies have demonstrated the usefulness of the English
auction in a restricted class of mechanisms. In a classic treatise, Milgrom and
Weber (1982) show that the English auction is optimal among the four standard
auction forms when the valuations are affiliated, a natural assumption in many
auction scenarios.22 In the same model, Lopomo (1998, 2001) demonstrates that
the English auction features robustness in a sense that it is optimal among simple
sequential auctions and in a class of posteriorly implementable auctions (a concept
due to Green and Laffont, 1987).
Posterior implementability requires that the buyers’ behavior is regret-free in
a sense that they would not want to change their behavior even if they knew the
outcome of the mechanism. This property is at the heart of the robustness of the
English auction and the Vickrey auction.23 It is partly driving also our results.
Due to posterior implementability, running the English or the Vickrey auction
twice in a row rather than just once will not affect the outcome. This implies
that the English auction is idempotent in the sense of Lemma 1. But this is only
a necessary condition of a feasible auction. On the sufficient side, one needs to
guarantee that the seller cannot commit to any more profitable auction at the ex
post stage, given the information that is generated by the mechanism. That the
English auction does well also in this respect is not a consequence of posterior
or ex post implementability. For example, the Vickrey auction reveals too much
information as also the winner’s type is revealed. Thus the unique feasibility of
the English auction is due to both its posterior implementability and its innate
informational properties.
But one can also see the situation the other way around. Since Wilson (1987),
a recurrent theme in mechanism design literature has been that a good theory
should not rely too heavily on assumptions of common knowledge. Motivated
by the Wilson Doctrine, many authors have proceeded by imposing conditions
such as ex post implementability on choice rules, as explained by Chung and Ely
(2007), which presumably mirrors detail-freeness. It is, however, not completely
clear what kind of behavioral implications does the restriction have. Is there a
theoretical reason arising from the players’ behavior that justifies detail-freeness
as an assumption? Our model provides one such motivation: detail-freeness is bad
if the seller cannot commit to the mechanism. In the absence of commitment, an
implementable mechanism needs to have a degree of vagueness and hence only the
ex post implementable English auction is feasible. Note that this applies also to
the case of correlated valuations.24
22 Including the English, Vickrey, Dutch, and first-price auctions. However, Matthews (1987)
and Maskin and Riley (1984) show that risk-aversion reverses the ranking.
23 The English auction also satisfies a stronger condition of ex post implementability: that one
does not want to change his own behavior even if one knows the behavior of the other players.
See e.g. Bergeman and Morris (2005, 2008).
24 Chung and Ely (2007) provide a related motivation, stemming from the seller’s uncertainty
aversion.
16