1,185 research outputs found
Truthful approximation mechanisms for restricted combinatorial auctions
When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness).
We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios
Characterizing Optimal Adword Auctions
We present a number of models for the adword auctions used for pricing
advertising slots on search engines such as Google, Yahoo! etc. We begin with a
general problem formulation which allows the privately known valuation per
click to be a function of both the identity of the advertiser and the slot. We
present a compact characterization of the set of all deterministic incentive
compatible direct mechanisms for this model. This new characterization allows
us to conclude that there are incentive compatible mechanisms for this auction
with a multi-dimensional type-space that are {\em not} affine maximizers. Next,
we discuss two interesting special cases: slot independent valuation and slot
independent valuation up to a privately known slot and zero thereafter. For
both of these special cases, we characterize revenue maximizing and efficiency
maximizing mechanisms and show that these mechanisms can be computed with a
worst case computational complexity and respectively,
where is number of bidders and is number of slots. Next, we
characterize optimal rank based allocation rules and propose a new mechanism
that we call the customized rank based allocation. We report the results of a
numerical study that compare the revenue and efficiency of the proposed
mechanisms. The numerical results suggest that customized rank-based allocation
rule is significantly superior to the rank-based allocation rules.Comment: 29 pages, work was presented at a) Second Workshop on Sponsored
Search Auctions, Ann Arbor, MI b) INFORMS Annual Meeting, Pittsburgh c)
Decision Sciences Seminar, Fuqua School of Business, Duke Universit
Optimal Mechanism Design with Flexible Consumers and Costly Supply
The problem of designing a profit-maximizing, Bayesian incentive compatible
and individually rational mechanism with flexible consumers and costly
heterogeneous supply is considered. In our setup, each consumer is associated
with a flexibility set that describes the subset of goods the consumer is
equally interested in. Each consumer wants to consume one good from its
flexibility set. The flexibility set of a consumer and the utility it gets from
consuming a good from its flexibility set are its private information. We adopt
the flexibility model of [1] and focus on the case of nested flexibility sets
-- each consumer's flexibility set can be one of k nested sets. Examples of
settings with this inherent nested structure are provided. On the supply side,
we assume that the seller has an initial stock of free supply but it can
purchase more goods for each of the nested sets at fixed exogenous prices. We
characterize the allocation and purchase rules for a profit-maximizing,
Bayesian incentive compatible and individually rational mechanism as the
solution to an integer program. The optimal payment function is pinned down by
the optimal allocation rule in the form of an integral equation. We show that
the nestedness of flexibility sets can be exploited to obtain a simple
description of the optimal allocations, purchases and payments in terms of
thresholds that can be computed through a straightforward iterative procedure.Comment: 8 pages. arXiv admin note: text overlap with arXiv:1607.0252
Expressiveness and Robustness of First-Price Position Auctions
Since economic mechanisms are often applied to very different instances of
the same problem, it is desirable to identify mechanisms that work well in a
wide range of circumstances. We pursue this goal for a position auction setting
and specifically seek mechanisms that guarantee good outcomes under both
complete and incomplete information. A variant of the generalized first-price
mechanism with multi-dimensional bids turns out to be the only standard
mechanism able to achieve this goal, even when types are one-dimensional. The
fact that expressiveness beyond the type space is both necessary and sufficient
for this kind of robustness provides an interesting counterpoint to previous
work on position auctions that has highlighted the benefits of simplicity. From
a technical perspective our results are interesting because they establish
equilibrium existence for a multi-dimensional bid space, where standard
techniques break down. The structure of the equilibrium bids moreover provides
an intuitive explanation for why first-price payments may be able to support
equilibria in a wider range of circumstances than second-price payments
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