1,109 research outputs found
Mechanisms for Multi-unit Combinatorial Auctions with a Few Distinct Goods
We design and analyze deterministic truthful approximation mechanisms for multi-unit Combinatorial Auctions involving only a constant number of distinct goods, each in arbitrary limited supply. Prospective buyers (bidders) have preferences over multisets of items, i.e., for more than one unit per distinct good. Our objective is to determine allocations of multisets that maximize the Social Welfare. Our main results are for multi-minded and submodular bidders. In the first setting each bidder has a positive value for being allocated one multiset from a prespecified demand set of alternatives. In the second setting each bidder is associated to a submodular valuation function that defines his value for the multiset he is allocated. For multi-minded bidders, we design a truthful Fptas that fully optimizes the Social Welfare, while violating the supply constraints on goods within factor (1 + ), for any fixed > 0 (i.e., the approximation applies to the constraints and not to the Social Welfare). This result is best possible, in that full optimization is impossible without violating the supply constraints. For submodular bidders, we obtain a Ptas that approximates the optimum Social Welfare within factor (1 + ), for any fixed > 0, without violating the supply constraints. This result is best possible as well. Our allocation algorithms are Maximal-in-Range and yield truthful mechanisms, when paired with Vickrey-Clarke-Groves payments
On the Efficiency of the Walrasian Mechanism
Central results in economics guarantee the existence of efficient equilibria
for various classes of markets. An underlying assumption in early work is that
agents are price-takers, i.e., agents honestly report their true demand in
response to prices. A line of research in economics, initiated by Hurwicz
(1972), is devoted to understanding how such markets perform when agents are
strategic about their demands. This is captured by the \emph{Walrasian
Mechanism} that proceeds by collecting reported demands, finding clearing
prices in the \emph{reported} market via an ascending price t\^{a}tonnement
procedure, and returns the resulting allocation. Similar mechanisms are used,
for example, in the daily opening of the New York Stock Exchange and the call
market for copper and gold in London.
In practice, it is commonly observed that agents in such markets reduce their
demand leading to behaviors resembling bargaining and to inefficient outcomes.
We ask how inefficient the equilibria can be. Our main result is that the
welfare of every pure Nash equilibrium of the Walrasian mechanism is at least
one quarter of the optimal welfare, when players have gross substitute
valuations and do not overbid. Previous analysis of the Walrasian mechanism
have resorted to large market assumptions to show convergence to efficiency in
the limit. Our result shows that approximate efficiency is guaranteed
regardless of the size of the market
Efficiency Guarantees in Auctions with Budgets
In settings where players have a limited access to liquidity, represented in
the form of budget constraints, efficiency maximization has proven to be a
challenging goal. In particular, the social welfare cannot be approximated by a
better factor then the number of players. Therefore, the literature has mainly
resorted to Pareto-efficiency as a way to achieve efficiency in such settings.
While successful in some important scenarios, in many settings it is known that
either exactly one incentive-compatible auction that always outputs a
Pareto-efficient solution, or that no truthful mechanism can always guarantee a
Pareto-efficient outcome. Traditionally, impossibility results can be avoided
by considering approximations. However, Pareto-efficiency is a binary property
(is either satisfied or not), which does not allow for approximations.
In this paper we propose a new notion of efficiency, called \emph{liquid
welfare}. This is the maximum amount of revenue an omniscient seller would be
able to extract from a certain instance. We explain the intuition behind this
objective function and show that it can be 2-approximated by two different
auctions. Moreover, we show that no truthful algorithm can guarantee an
approximation factor better than 4/3 with respect to the liquid welfare, and
provide a truthful auction that attains this bound in a special case.
Importantly, the liquid welfare benchmark also overcomes impossibilities for
some settings. While it is impossible to design Pareto-efficient auctions for
multi-unit auctions where players have decreasing marginal values, we give a
deterministic -approximation for the liquid welfare in this setting
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
Combinatorial auctions for electronic business
Combinatorial auctions (CAs) have recently generated significant interest as an automated mechanism for buying and selling bundles of goods. They are proving to be extremely useful in numerous e-business applications such as e-selling, e-procurement, e-logistics, and B2B exchanges. In this article, we introduce combinatorial auctions and bring out important issues in the design of combinatorial auctions. We also highlight important contributions in current research in this area. This survey emphasizes combinatorial auctions as applied to electronic business situations
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