539,718 research outputs found
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
Average-case Approximation Ratio of Scheduling without Payments
Apart from the principles and methodologies inherited from Economics and Game
Theory, the studies in Algorithmic Mechanism Design typically employ the
worst-case analysis and approximation schemes of Theoretical Computer Science.
For instance, the approximation ratio, which is the canonical measure of
evaluating how well an incentive-compatible mechanism approximately optimizes
the objective, is defined in the worst-case sense. It compares the performance
of the optimal mechanism against the performance of a truthful mechanism, for
all possible inputs.
In this paper, we take the average-case analysis approach, and tackle one of
the primary motivating problems in Algorithmic Mechanism Design -- the
scheduling problem [Nisan and Ronen 1999]. One version of this problem which
includes a verification component is studied by [Koutsoupias 2014]. It was
shown that the problem has a tight approximation ratio bound of (n+1)/2 for the
single-task setting, where n is the number of machines. We show, however, when
the costs of the machines to executing the task follow any independent and
identical distribution, the average-case approximation ratio of the mechanism
given in [Koutsoupias 2014] is upper bounded by a constant. This positive
result asymptotically separates the average-case ratio from the worst-case
ratio, and indicates that the optimal mechanism for the problem actually works
well on average, although in the worst-case the expected cost of the mechanism
is Theta(n) times that of the optimal cost
Social Status and Badge Design
Many websites rely on user-generated content to provide value to consumers.
These websites typically incentivize participation by awarding users badges
based on their contributions. While these badges typically have no explicit
value, they act as symbols of social status within a community. In this paper,
we consider the design of badge mechanisms for the objective of maximizing the
total contributions made to a website. Users exert costly effort to make
contributions and, in return, are awarded with badges. A badge is only valued
to the extent that it signals social status and thus badge valuations are
determined endogenously by the number of users who earn each badge. The goal of
this paper is to study the design of optimal and approximately badge mechanisms
under these status valuations. We characterize badge mechanisms by whether they
use a coarse partitioning scheme, i.e. awarding the same badge to many users,
or use a fine partitioning scheme, i.e. awarding a unique badge to most users.
We find that the optimal mechanism uses both fine partitioning and coarse
partitioning. When status valuations exhibit a decreasing marginal value
property, we prove that coarse partitioning is a necessary feature of any
approximately optimal mechanism. Conversely, when status valuations exhibit an
increasing marginal value property, we prove that fine partitioning is
necessary for approximate optimality
MECHANISM DESIGN WITH GENERAL UTILITIES
This thesis studies mechanism design from an optimization perspective.
Our main contribution is to characterize fundamental structural properties of optimization problems arising
in mechanism design and to exploit them to design general frameworks and techniques for efficiently solving
the underlying problems. Not only do our characterizations allow for efficient computation, they also reveal
qualitative characteristics of optimal mechanisms which are important even from a non-computational
standpoint. Furthermore, most of our techniques are widely applicable to optimization problems outside of
mechanism design such as online algorithms or stochastic optimization.
Our frameworks can be summarized as follows. When the input to an optimization problem (e.g., a mechanism
design problem) comes from independent sources (e.g., independent agents), the complexity of the problem can
be exponentially reduced by (i) decomposing the problem into smaller subproblems, each one involving one
input source, (ii) simultaneously optimizing the subproblems subject to certain relaxation of coupling
constraints, and (iii) combining the solutions of the subproblems in a certain way to obtain an
(approximately) optimal solution for the original problem.
We use our proposed framework to construct optimal or approximately optimal mechanisms for several settings
previously considered in the literature and to improve upon the best previously known results. We also
present applications of our techniques to non-mechanism design problems such as online stochastic generalized
assignment problem which itself captures online and stochastic versions of various other problems such as
resource allocation and job scheduling
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