42 research outputs found
Revenue Loss in Shrinking Markets
We analyze the revenue loss due to market shrinkage. Specifically, consider a
simple market with one item for sale and bidders whose values are drawn
from some joint distribution. Suppose that the market shrinks as a single
bidder retires from the market. Suppose furthermore that the value of this
retiring bidder is fixed and always strictly smaller than the values of the
other players. We show that even this slight decrease in competition might
cause a significant fall of a multiplicative factor of
in the revenue that can be obtained by a dominant
strategy ex-post individually rational mechanism.
In particular, our results imply a solution to an open question that was
posed by Dobzinski, Fu, and Kleinberg [STOC'11]
Optimal Auctions for Correlated Buyers with Sampling
Cr\'emer and McLean [1985] showed that, when buyers' valuations are drawn
from a correlated distribution, an auction with full knowledge on the
distribution can extract the full social surplus. We study whether this
phenomenon persists when the auctioneer has only incomplete knowledge of the
distribution, represented by a finite family of candidate distributions, and
has sample access to the real distribution. We show that the naive approach
which uses samples to distinguish candidate distributions may fail, whereas an
extended version of the Cr\'emer-McLean auction simultaneously extracts full
social surplus under each candidate distribution. With an algebraic argument,
we give a tight bound on the number of samples needed by this auction, which is
the difference between the number of candidate distributions and the dimension
of the linear space they span
Vickrey Auctions for Irregular Distributions
The classic result of Bulow and Klemperer \cite{BK96} says that in a
single-item auction recruiting one more bidder and running the Vickrey auction
achieves a higher revenue than the optimal auction's revenue on the original
set of bidders, when values are drawn i.i.d. from a regular distribution. We
give a version of Bulow and Klemperer's result in settings where bidders'
values are drawn from non-i.i.d. irregular distributions. We do this by
modeling irregular distributions as some convex combination of regular
distributions. The regular distributions that constitute the irregular
distribution correspond to different population groups in the bidder
population. Drawing a bidder from this collection of population groups is
equivalent to drawing from some convex combination of these regular
distributions. We show that recruiting one extra bidder from each underlying
population group and running the Vickrey auction gives at least half of the
optimal auction's revenue on the original set of bidders
Brief Announcement: Bayesian Auctions with Efficient Queries
Generating good revenue is one of the most important problems in Bayesian auction design, and many (approximately) optimal dominant-strategy incentive compatible (DSIC) Bayesian mechanisms have been constructed for various auction settings. However, most existing studies do not consider the complexity for the seller to carry out the mechanism. It is assumed that the seller knows "each single bit" of the distributions and is able to optimize perfectly based on the entire distributions. Unfortunately this is a strong assumption and may not hold in reality: for example, when the value distributions have exponentially large supports or do not have succinct representations.
In this work we consider, for the first time, the query complexity of Bayesian mechanisms. We only allow the seller to have limited oracle accesses to the players\u27 value distributions, via quantile queries and value queries. For a large class of auction settings, we prove logarithmic lower-bounds for the query complexity for any DSIC Bayesian mechanism to be of any constant approximation to the optimal revenue. For single-item auctions and multi-item auctions with unit-demand or additive valuation functions, we prove tight upper-bounds via efficient query schemes, without requiring the distributions to be regular or have monotone hazard rate. Thus, in those auction settings the seller needs to access much less than the full distributions in order to achieve approximately optimal revenue
The Value of Information Concealment
We consider a revenue optimizing seller selling a single item to a buyer, on
whose private value the seller has a noisy signal. We show that, when the
signal is kept private, arbitrarily more revenue could potentially be extracted
than if the signal is leaked or revealed. We then show that, if the seller is
not allowed to make payments to the buyer, the gap between the two is bounded
by a multiplicative factor of 3, if the value distribution conditioning on each
signal is regular. We give examples showing that both conditions are necessary
for a constant bound to hold.
We connect this scenario to multi-bidder single-item auctions where bidders'
values are correlated. Similarly to the setting above, we show that the revenue
of a Bayesian incentive compatible, ex post individually rational auction can
be arbitrarily larger than that of a dominant strategy incentive compatible
auction, whereas the two are no more than a factor of 5 apart if the auctioneer
never pays the bidders and if each bidder's value conditioning on the others'
is drawn according to a regular distribution. The upper bounds in both settings
degrade gracefully when the distribution is a mixture of a small number of
regular distributions