2,253 research outputs found
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
Maximizing Revenue in the Presence of Intermediaries
We study the mechanism design problem of selling items to unit-demand
buyers with private valuations for the items. A buyer either participates
directly in the auction or is represented by an intermediary, who represents a
subset of buyers. Our goal is to design robust mechanisms that are independent
of the demand structure (i.e. how the buyers are partitioned across
intermediaries), and perform well under a wide variety of possible contracts
between intermediaries and buyers.
We first study the case of identical items where each buyer draws its
private valuation for an item i.i.d. from a known -regular
distribution. We construct a robust mechanism that, independent of the demand
structure and under certain conditions on the contracts between intermediaries
and buyers, obtains a constant factor of the revenue that the mechanism
designer could obtain had she known the buyers' valuations. In other words, our
mechanism's expected revenue achieves a constant factor of the optimal welfare,
regardless of the demand structure. Our mechanism is a simple posted-price
mechanism that sets a take-it-or-leave-it per-item price that depends on
and the total number of buyers, but does not depend on the demand structure or
the downstream contracts.
Next we generalize our result to the case when the items are not identical.
We assume that the item valuations are separable. For this case, we design a
mechanism that obtains at least a constant fraction of the optimal welfare, by
using a menu of posted prices. This mechanism is also independent of the demand
structure, but makes a relatively stronger assumption on the contracts between
intermediaries and buyers, namely that each intermediary prefers outcomes with
a higher sum of utilities of the subset of buyers represented by it
Prior-Independent Auctions for Heterogeneous Bidders
We study the design of prior-independent auctions in a setting with
heterogeneous bidders. In particular, we consider the setting of selling to
bidders whose values are drawn from independent but not necessarily
identical distributions. We work in the robust auction design regime, where we
assume the seller has no knowledge of the bidders' value distributions and must
design a mechanism that is prior-independent. While there have been many strong
results on prior-independent auction design in the i.i.d. setting, not much is
known for the heterogeneous setting, even though the latter is of significant
practical importance. Unfortunately, no prior-independent mechanism can hope to
always guarantee any approximation to Myerson's revenue in the heterogeneous
setting; similarly, no prior-independent mechanism can consistently do better
than the second-price auction. In light of this, we design a family of
(parametrized) randomized auctions which approximates at least one of these
benchmarks: For heterogeneous bidders with regular value distributions, our
mechanisms either achieve a good approximation of the expected revenue of an
optimal mechanism (which knows the bidders' distributions) or exceeds that of
the second-price auction by a certain multiplicative factor. The factor in the
latter case naturally trades off with the approximation ratio of the former
case. We show that our mechanism is optimal for such a trade-off between the
two cases by establishing a matching lower bound. Our result extends to selling
identical items to heterogeneous bidders with an additional -factor in our trade-off between the two cases
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