490 research outputs found
Bundling Equilibrium in Combinatorial auctions
This paper analyzes individually-rational ex post equilibrium in the VC
(Vickrey-Clarke) combinatorial auctions. If is a family of bundles of
goods, the organizer may restrict the participants by requiring them to submit
their bids only for bundles in . The -VC combinatorial auctions
(multi-good auctions) obtained in this way are known to be
individually-rational truth-telling mechanisms. In contrast, this paper deals
with non-restricted VC auctions, in which the buyers restrict themselves to
bids on bundles in , because it is rational for them to do so. That is,
it may be that when the buyers report their valuation of the bundles in
, they are in an equilibrium. We fully characterize those that
induce individually rational equilibrium in every VC auction, and we refer to
the associated equilibrium as a bundling equilibrium. The number of bundles in
represents the communication complexity of the equilibrium. A special
case of bundling equilibrium is partition-based equilibrium, in which
is a field, that is, it is generated by a partition. We analyze the tradeoff
between communication complexity and economic efficiency of bundling
equilibrium, focusing in particular on partition-based equilibrium
Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned
Optimal mechanism design enjoys a beautiful and well-developed theory, and
also a number of killer applications. Rules of thumb produced by the field
influence everything from how governments sell wireless spectrum licenses to
how the major search engines auction off online advertising. There are,
however, some basic problems for which the traditional optimal mechanism design
approach is ill-suited --- either because it makes overly strong assumptions,
or because it advocates overly complex designs. The thesis of this paper is
that approximately optimal mechanisms allow us to reason about fundamental
questions that seem out of reach of the traditional theory.
This survey has three main parts. The first part describes the approximately
optimal mechanism design paradigm --- how it works, and what we aim to learn by
applying it. The second and third parts of the survey cover two case studies,
where we instantiate the general design paradigm to investigate two basic
questions. In the first example, we consider revenue maximization in a
single-item auction with heterogeneous bidders. Our goal is to understand if
complexity --- in the sense of detailed distributional knowledge --- is an
essential feature of good auctions for this problem, or alternatively if there
are simpler auctions that are near-optimal. The second example considers
welfare maximization with multiple items. Our goal here is similar in spirit:
when is complexity --- in the form of high-dimensional bid spaces --- an
essential feature of every auction that guarantees reasonable welfare? Are
there interesting cases where low-dimensional bid spaces suffice?Comment: Based on a talk given by the author at the 15th ACM Conference on
Economics and Computation (EC), June 201
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
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