Auction Design without Commitment

common (see Rothkopf et al., 1990).

Our argument is closely related to the famous Coase conjecture, arguing that
in the one buyer scenario the seller without commitment power is forced to sell
the good with the price equal to the least possible valuation of the buyer (see Gul
et al., 1986; Fudenberg et al., 1985, Ausubel et al., 2002). For the same reason
the English auction is robust against commitment problems. The English auction
reveals (i) the buyer with the highest valuation (the winner), and (ii) valuations of
all but the winner. Since the winner is known to have the highest valuation once
the output has materialized, the seller cannot commit to sell the good anyone but
the winner. Hence, as under the Coase conjecture, the seller is forced to sell the
good to the winner with his least possible valuation which is equal to the second
highest valuation of the buyers, already revealed by the mechanism. In the one
buyer case, this argument collapses back to the standard Coase conjecture.⁷

Literature on mechanism design without commitment The distin-
guishing feature of this paper in the literature on mechanism design without com-
mitment is that it does not put any restrictions on mechanisms that are technically
feasible for the designer neither at the ex ante nor at the ex post stage; the prob-
lem is genuinely that of commitment. For example, there are neither discounting
nor other waiting costs.

On the modeling side, the novelty of the paper is that the commitment problem
is studied via revelation games rather than as a bottom-up extensive form game.
The reason why we focus on a reduced form expression of the true underlying game
is foremost expositional. But we do so also because we are not interested in identi-
fying all the equilibria of the game. All features of the model, i.e., multitudity of
players, unboundedness of redesign rounds, and richness of the action sets (= all
mechanisms) hint that this set would not be small. Hence, we follow the standard
mechanism design avenue by assuming (implicitly) that truthfulness, whenever
appropriately defined, is a focal feature of an equilibrium. In our framework, this
means that it is the truthful equilibrium of the reduced form of the continuation
game that is relevant. Hence, as in the standard mechanism design literature, we
implicitly assume that the seller can choose the continuation equilibrium of the
game. The key problem of the seller is to choose the continuation equilibrium in
a dynamically consistent way when information is being revealed along the play.
This is the interpretation of our equilibrium concept.

It should be emphasized that the methods developed in this work do not at-
tempt to challenge or provide an alternative to the standard equilibrium tech-
niques. Rather, the modeling here is meant to be consistent with them. The only
reason for focusing on the reduced form expressions is to penetrate into the core
aspects of the problem.

Of course, useful results can also be obtained by appealing to standard equi-
librium techniques. However, this requires somewhat more restricted domain.
McAfee and Vincent (1997) study an auction designer who can set a positive re-

⁷ For studies on the no gap -case in the durable good monopoly scenario, see Ausubel and
Deneckere (1989a,b)

<<   4   5   6   7   8   9   10   >>

More intriguing information