2 research outputs found
Can Buyers Reveal for a Better Deal?
We study small-scale market interactions in which buyers are allowed to
credibly reveal partial information about their types to the seller. Previous
recent work has studied the special case where there is one buyer and one good,
showing that such communication can simultaneously improve social welfare and
ex ante buyer utility. With multiple buyers, we find that the buyer-optimal
signalling schemes from the one-buyer case are actually harmful to buyer
welfare. Moreover, we prove several impossibility results showing that, with
either multiple i.i.d. buyers or multiple i.i.d. goods, maximizing buyer
utility can be at odds with social efficiency, which is a surprising contrast
to the one-buyer, one-good case. Finally, we investigate the computational
tractability of implementing desirable equilibrium outcomes. We find that, even
with one buyer and one good, optimizing buyer utility is generally NP-hard, but
tractable in a practical restricted setting
The Limits of an Information Intermediary in Auction Design
We study the limits of an information intermediary in Bayesian auctions.
Formally, we consider the standard single-item auction, with a
revenue-maximizing seller and buyers with independent private values; in
addition, we now have an intermediary who knows the buyers' true values, and
can map these to a public signal so as to try to increase buyer surplus. This
model was proposed by Bergemann et al., who present a signaling scheme for the
single-buyer setting that raises the optimal consumer surplus, by guaranteeing
the item is always sold while ensuring the seller gets the same revenue as
without signaling. Our work aims to understand how this result ports to the
setting with multiple buyers.
Our first result is an impossibility: We show that such a signaling scheme
need not exist even for buyers with -point valuation distributions.
Indeed, no signaling scheme can always allocate the item to the highest-valued
buyer while preserving any non-trivial fraction of the original consumer
surplus; further, no signaling scheme can achieve consumer surplus better than
a factor of compared to the maximum achievable. These results are
existential (and not computational) impossibilities, and thus provide a sharp
separation between the single and multi-buyer settings.
On the positive side, for discrete valuation distributions, we develop
signaling schemes with good approximation guarantees for the consumer surplus
compared to the maximum achievable, in settings where either the number of
agents, or the support size of valuations, is small. Formally, for i.i.d.
buyers, we present an -approximation where is the
support size of the valuations. Moreover, for general distributions, we present
an -approximation. Our signaling schemes are
conceptually simple and computable in polynomial (in and ) time