Auction Design without Commitment

mechanism ex post, they will adjust their play accordingly at the interim stage.⁴
Consequently, incentive compatibility of the mechanism breaks down.⁵

We analyze auction design under the benchmark hypothesis that parties do
not have any commitment power: the seller may freely change the auction rules
as many times as she wishes, and the buyers can leave the auction at any point
of the game. A novel framework is developed to analyze the problem. The idea
is to first apply the standard revelation argument to isolate possible solutions to
the seller’s mechanism selection problem, and then restrict the solutions further
with the consistency and optimization conditions that reflect the seller’s dynamic
behavior.

More precisely, we decompose the mechanism into an information processing
device and an implementation device. The information processing device can be
interpreted as a machine or a mediator that transforms the messages of the buyers
into an output - a public signal - in a reliable and secure way. No technological
constraints are imposed on the form of this information processing device. The
task of the implementation device is to choose a physical outcome contingent on
the signal that is generated by the information processing device. One should note
that decomposability is not a restriction on feasible mechanisms: any mechanism
can be decomposed in a unique way into the prescribed information processing and
implementation devices. The crucial assumption - and the reason for decomposing
the mechanism into two parts - is that the seller cannot commit to the implemen-
tation device. That is, ex post she can invoke another (composite) mechanism
rather than implement the outcome suggested by the implementation device.

The sellers mechanism design behavior is captured by a rule σ that identifies,
for each seller’s belief p, a mechanism σ(p) that the seller implements under belief
p. Two conditions are imposed on the rule σ that guarantee that a sequentially
rational seller can commit to it. The first is that the rule has to be internally
consistent: selecting a mechanism according to the rule should not be in conflict
with obeying the rule at later stages of the game. The second condition is that
the rule needs to be optimal : under any belief p the seller should not be able to
profit by deviating from σ(p) within the class of mechanisms that she can commit
to, given that she obeys σ in the future. The latter property is dubbed as the
one-deviation property. A stationarity condition, which requires that the rule is
not conditioned on payoff irrelevant information, is also assumed.

Our main result is that the payoff and information structure of any feasible
mechanism, i.e., mechanism chosen by a stationary and consistent mechanism
selection rule that also satisfies the one-deviation property, is the English auction
(indexed by a tie-breaking rule). Conversely, the rule that always chooses the
English auction is consistent, stationary, and meets the one-deviation property.
Thus the English auction is (essentially) the unique mechanism that the seller
can implement without commitment.⁶ Our model may therefore explain why the
Vickrey or other prominent auction forms are rare but the English auctions are

⁴In Freixas et al. (1985) this is called the ratchet effect.

⁵Unless all the surplus is extracted from the buyers a la Cremer and McLean (1988). But
this requires the buyers to commit to participate ex post.

⁶ "Essentially" means that the auction may also reveal some immaterial information.

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