Truthful Mechanisms for OneParameter Agents
Aaron Archer
´
Eva Tardos
Abstract
In this paper, we show how to design
truthful
(dominant
strategy) mechanisms for several combinatorial problems
where each agent’s secret data is naturally expressed by a
single positive real number. The goal of the mechanisms
we consider is to allocate
loads
placed on the agents, and
an agent’s secret data is the cost she incurs per unit load.
We give an exact characterization for the algorithms that
can be used to design truthful mechanisms for such load
balancing problems using appropriate side payments.
We use our characterization to design polynomial time
truthful mechanisms for several problems in combinato
rial optimization to which the celebrated VCG mechanism
does not apply. For scheduling related parallel machines
(
), we give a 3approximation mechanism based
on randomized rounding of the optimal fractional solution.
This problem is NPcomplete, and the standard approxima
tion algorithms (greedy loadbalancing or the PTAS) can
not be used in truthful mechanisms. We show our mecha
nism to be
frugal
, in that the total payment needed is only
a logarithmic factor more than the actual costs incurred
by the machines, unless one machine dominates the total
processing power.
We also give truthful mechanisms for
maximum flow,
(scheduling related machines to
minimize the sum of completion times), optimizing an affine
function over a fixed set, and special cases of uncapacitated
facility location. In addition, for
(minimizing
the weighted sum of completion times), we prove a lower
bound of
for the best approximation ratio achievable by
a truthful mechanism.
1
Introduction
In economics, social choice theory addresses the prob
lem of aggregating individuals’ preferences to make a group
Operations Research Department, Cornell University, Ithaca, NY
14853.
Email:
[email protected]
.
Supported by the
Fannie and John Hertz Foundation.
Computer Science Department, Cornell University, Ithaca, NY 14853.
Email:
[email protected]
Research supported in part by NSF
grant CCR9700163 and ONR grant N000149810589.
decision.
As indicated by Arrow’s impossibility theorem
for satisfactory voting systems [2], this is a thorny problem.
It is further complicated by the possibility that the partici
pants (usually called
players
or
agents
) might try to manip
ulate the system by misrepresenting their preferences. The
field of
mechanism design
recognizes this game theoretic
aspect and aims to arrange things so that a rational player
will never find it in her selfinterest to lie. Mechanisms that
do this are called
strategyproof
or
truthful
.
Because of some stifling negative results that apply when
the agents’ preferences can be arbitrary, it is common to re
strict the domain of preferences by assuming
additive sepa
rability
. Each agent is assumed to incur some intrinsic ben
efit or loss (called its
valuation
) depending on the outcome
of the mechanism, and this valuation is expressible in some
common unit of currency. The mechanism also makes
pay
ments
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 Fall '08
 cis620
 WI, Approximation algorithm, truthful mechanisms

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