378 research outputs found
A Truthful Mechanism for the Generalized Assignment Problem
We propose a truthful-in-expectation, -approximation mechanism for a
strategic variant of the generalized assignment problem (GAP). In GAP, a set of
items has to be optimally assigned to a set of bins without exceeding the
capacity of any singular bin. In the strategic variant of the problem we study,
values for assigning items to bins are the private information of bidders and
the mechanism should provide bidders with incentives to truthfully report their
values. The approximation ratio of the mechanism is a significant improvement
over the approximation ratio of the existing truthful mechanism for GAP.
The proposed mechanism comprises a novel convex optimization program as the
allocation rule as well as an appropriate payment rule. To implement the convex
program in polynomial time, we propose a fractional local search algorithm
which approximates the optimal solution within an arbitrarily small error
leading to an approximately truthful-in-expectation mechanism. The presented
algorithm improves upon the existing optimization algorithms for GAP in terms
of simplicity and runtime while the approximation ratio closely matches the
best approximation ratio given for GAP when all inputs are publicly known.Comment: 18 pages, Earlier version accepted at WINE 201
Reallocation Mechanisms
We consider reallocation problems in settings where the initial endowment of
each agent consists of a subset of the resources. The private information of
the players is their value for every possible subset of the resources. The goal
is to redistribute resources among agents to maximize efficiency. Monetary
transfers are allowed, but participation is voluntary.
We develop incentive-compatible, individually-rational and budget balanced
mechanisms for several classic settings, including bilateral trade, partnership
dissolving, Arrow-Debreu markets, and combinatorial exchanges. All our
mechanisms (except one) provide a constant approximation to the optimal
efficiency in these settings, even in ones where the preferences of the agents
are complex multi-parameter functions
Reducing Revenue to Welfare Maximization: Approximation Algorithms and other Generalizations
It was recently shown in [http://arxiv.org/abs/1207.5518] that revenue
optimization can be computationally efficiently reduced to welfare optimization
in all multi-dimensional Bayesian auction problems with arbitrary (possibly
combinatorial) feasibility constraints and independent additive bidders with
arbitrary (possibly combinatorial) demand constraints. This reduction provides
a poly-time solution to the optimal mechanism design problem in all auction
settings where welfare optimization can be solved efficiently, but it is
fragile to approximation and cannot provide solutions to settings where welfare
maximization can only be tractably approximated. In this paper, we extend the
reduction to accommodate approximation algorithms, providing an approximation
preserving reduction from (truthful) revenue maximization to (not necessarily
truthful) welfare maximization. The mechanisms output by our reduction choose
allocations via black-box calls to welfare approximation on randomly selected
inputs, thereby generalizing also our earlier structural results on optimal
multi-dimensional mechanisms to approximately optimal mechanisms. Unlike
[http://arxiv.org/abs/1207.5518], our results here are obtained through novel
uses of the Ellipsoid algorithm and other optimization techniques over {\em
non-convex regions}
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