23 research outputs found
Third-Party Data Providers Ruin Simple Mechanisms
Motivated by the growing prominence of third-party data providers in online
marketplaces, this paper studies the impact of the presence of third-party data
providers on mechanism design. When no data provider is present, it has been
shown that simple mechanisms are "good enough" -- they can achieve a constant
fraction of the revenue of optimal mechanisms. The results in this paper
demonstrate that this is no longer true in the presence of a third-party data
provider who can provide the bidder with a signal that is correlated with the
item type. Specifically, even with a single seller, a single bidder, and a
single item of uncertain type for sale, the strategies of pricing each
item-type separately (the analog of item pricing for multi-item auctions) and
bundling all item-types under a single price (the analog of grand bundling) can
both simultaneously be a logarithmic factor worse than the optimal revenue.
Further, in the presence of a data provider, item-type partitioning
mechanisms---a more general class of mechanisms which divide item-types into
disjoint groups and offer prices for each group---still cannot achieve within a
factor of the optimal revenue. Thus, our results highlight that the
presence of a data-provider forces the use of more complicated mechanisms in
order to achieve a constant fraction of the optimal revenue
Optimal Multi-Unit Mechanisms with Private Demands
In the multi-unit pricing problem, multiple units of a single item are for
sale. A buyer's valuation for units of the item is ,
where the per unit valuation and the capacity are private information
of the buyer. We consider this problem in the Bayesian setting, where the pair
is drawn jointly from a given probability distribution. In the
\emph{unlimited supply} setting, the optimal (revenue maximizing) mechanism is
a pricing problem, i.e., it is a menu of lotteries. In this paper we show that
under a natural regularity condition on the probability distributions, which we
call \emph{decreasing marginal revenue}, the optimal pricing is in fact
\emph{deterministic}. It is a price curve, offering units of the item for a
price of , for every integer . Further, we show that the revenue as a
function of the prices is a \emph{concave} function, which implies that
the optimum price curve can be found in polynomial time. This gives a rare
example of a natural multi-parameter setting where we can show such a clean
characterization of the optimal mechanism. We also give a more detailed
characterization of the optimal prices for the case where there are only two
possible demands
Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity
We study the revenue maximization problem of a seller with n heterogeneous
items for sale to a single buyer whose valuation function for sets of items is
unknown and drawn from some distribution D. We show that if D is a distribution
over subadditive valuations with independent items, then the better of pricing
each item separately or pricing only the grand bundle achieves a
constant-factor approximation to the revenue of the optimal mechanism. This
includes buyers who are k-demand, additive up to a matroid constraint, or
additive up to constraints of any downwards-closed set system (and whose values
for the individual items are sampled independently), as well as buyers who are
fractionally subadditive with item multipliers drawn independently. Our proof
makes use of the core-tail decomposition framework developed in prior work
showing similar results for the significantly simpler class of additive buyers
[LY13, BILW14].
In the second part of the paper, we develop a connection between
approximately optimal simple mechanisms and approximate revenue monotonicity
with respect to buyers' valuations. Revenue non-monotonicity is the phenomenon
that sometimes strictly increasing buyers' values for every set can strictly
decrease the revenue of the optimal mechanism [HR12]. Using our main result, we
derive a bound on how bad this degradation can be (and dub such a bound a proof
of approximate revenue monotonicity); we further show that better bounds on
approximate monotonicity imply a better analysis of our simple mechanisms.Comment: Updated title and body to version included in TEAC. Adapted Theorem
5.2 to accommodate \eta-BIC auctions (versus exactly BIC
Pricing for Online Resource Allocation: Intervals and Paths
We present pricing mechanisms for several online resource allocation problems
which obtain tight or nearly tight approximations to social welfare. In our
settings, buyers arrive online and purchase bundles of items; buyers' values
for the bundles are drawn from known distributions. This problem is closely
related to the so-called prophet-inequality of Krengel and Sucheston and its
extensions in recent literature. Motivated by applications to cloud economics,
we consider two kinds of buyer preferences. In the first, items correspond to
different units of time at which a resource is available; the items are
arranged in a total order and buyers desire intervals of items. The second
corresponds to bandwidth allocation over a tree network; the items are edges in
the network and buyers desire paths.
Because buyers' preferences have complementarities in the settings we
consider, recent constant-factor approximations via item prices do not apply,
and indeed strong negative results are known. We develop static, anonymous
bundle pricing mechanisms.
For the interval preferences setting, we show that static, anonymous bundle
pricings achieve a sublogarithmic competitive ratio, which is optimal (within
constant factors) over the class of all online allocation algorithms, truthful
or not. For the path preferences setting, we obtain a nearly-tight logarithmic
competitive ratio. Both of these results exhibit an exponential improvement
over item pricings for these settings. Our results extend to settings where the
seller has multiple copies of each item, with the competitive ratio decreasing
linearly with supply. Such a gradual tradeoff between supply and the
competitive ratio for welfare was previously known only for the single item
prophet inequality
Simple and Approximately Optimal Pricing for Proportional Complementarities
We study a new model of complementary valuations, which we call "proportional
complementarities." In contrast to common models, such as hypergraphic
valuations, in our model, we do not assume that the extra value derived from
owning a set of items is independent of the buyer's base valuations for the
items. Instead, we model the complementarities as proportional to the buyer's
base valuations, and these proportionalities are known market parameters.
Our goal is to design a simple pricing scheme that, for a single buyer with
proportional complementarities, yields approximately optimal revenue. We define
a new class of mechanisms where some number of items are given away for free,
and the remaining items are sold separately at inflated prices. We find that
the better of such a mechanism and selling the grand bundle earns a
12-approximation to the optimal revenue for pairwise proportional
complementarities. This confirms the intuition that items should not be sold
completely separately in the presence of complementarities.
In the more general case, a buyer has a maximum of proportional positive
hypergraphic valuations, where a hyperedge in a given hypergraph describes the
boost to the buyer's value for item given by owning any set of items in
addition. The maximum-out-degree of such a hypergraph is , and is the
positive rank of the hypergraph. For valuations given by these parameters, our
simple pricing scheme is an -approximation.Comment: Appeared in the 2019 ACM Conference on Economics and Computation (ACM
EC '19