17 research outputs found
The power of verification for one-parameter agents
We initiate the study of mechanisms with verification for one-parameter agents. We give an algorithmic characterization of such mechanisms and show that they are provably better than mechanisms without verification, i.e., those previously considered in the literature. These results are obtained for a number of optimization problems motivated by the Internet and recently studied in the algorithmic mechanism design literature. The characterization can be regarded as an alternative approach to existing techniques to design truthful mechanisms. The construction of such mechanisms reduces to the construction of an algorithm satisfying certain âmonotonicityâ conditions which, for the case of verification, are much less stringent. In other words, verification makes the construction easier and the algorithm more efficient (both computationally and in terms of approximability)
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
A New Lower Bound for Deterministic Truthful Scheduling
We study the problem of truthfully scheduling tasks to selfish
unrelated machines, under the objective of makespan minimization, as was
introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the
current gap of on the approximation ratio of deterministic truthful
mechanisms is a notorious open problem in the field of algorithmic mechanism
design. We provide the first such improvement in more than a decade, since the
lower bounds of (for ) and (for ) by
Christodoulou et al. [SODA'07] and Koutsoupias and Vidali [MFCS'07],
respectively. More specifically, we show that the currently best lower bound of
can be achieved even for just machines; for we already get
the first improvement, namely ; and allowing the number of machines to
grow arbitrarily large we can get a lower bound of .Comment: 15 page
Creating incentives to prevent execution failures: an extension of VCG mechanism
When information or control in a multiagent planning system is private to the agents, they may misreport this information or refuse to execute an agreed outcome, in order to change the resulting end state of such a system to their benefit. In some domains this may result in an execution failure. We show that in such settings VCG mechanisms lose truthfulness, and that the
utility of truthful agents can become negative when using VCG payments (i.e., VCG is not strongly individually rational). To deal with this problem, we introduce an extended payment structure which takes into account the actual execution of the promised outcome. We show that this extended mechanism can guarantee a nonnegative utility and is (i) incentive compatible in a Nash equilibrium, and (ii) incentive compatible in dominant strategies if and only if all agents can be verified during execution
Deterministic Monotone Algorithms for Scheduling on Related Machines
We consider the problem of designing monotone deterministic algorithms for scheduling tasks on related machines in order to minimize the makespan. Several recent papers showed that monotonicity is a fundamental property to design truthful mechanisms for this scheduling problem.
We give both theoretical and experimental results. First of all we consider the case of two machines when speeds of the machines are restricted to be powers of a given constant c>0. We prove that algorithm Largest Processing Time (LPT) is monotone for any câ„2 while it is not monotone for câ€1.78; algorithm List Scheduling (LS), instead, is monotone only for c>2.
In the case of m>2 machines we restrict our attention to the class of âgreedy-likeâ monotone algorithms defined in [Vincenzo Auletta, Roberto De Prisco, Paolo Penna, Giuseppe Persiano, Deterministic truthful approximation mechanisms for scheduling related machines, in: Proceedings of 21st Annual Symposium on Theoretical Aspects of Computer Science. STACS â04, in: Lecture Notes in Computer Science, vol. 2996, Springer, 2004, pp. 608â619]. It has been shown that greedy-like monotone algorithms can be used to design a family of 2+Δ-approximate truthful mechanisms. In particular, in [Vincenzo Auletta, Roberto De Prisco, Paolo Penna, Giuseppe Persiano, Deterministic truthful approximation mechanisms for scheduling related machines, in: Proceedings of 21st Annual Symposium on Theoretical Aspects of Computer Science. STACS â04, in: Lecture Notes in Computer Science, vol. 2996, Springer, 2004, pp. 608â619], the greedy-like algorithm Uniform is proposed and it is proved that it is monotone when machine speeds are powers of a given integer constant c>0. In this paper we propose a new algorithm, called Uniform_RR, that is still monotone when speeds are powers of a given integer constant c>0 and we prove that its approximation factor is not worse than that of Uniform. We also experimentally compare the performance of Uniform, Uniform_RR, LPT, and several other monotone and greedy-like heuristics
The Anarchy of Scheduling Without Money
We consider the scheduling problem on n strategic unrelated machines when no payments are allowed, under the objective of minimizing the makespan. We adopt the model introduced in [Koutsoupias 2014] where a machine is bound by her declarations in the sense that if she is assigned a particular job then she will have to execute it for an amount of time at least equal to the one she reported, even if her private, true processing capabilities are actually faster. We provide a (non-truthful) randomized algorithm whose pure Price of Anarchy is arbitrarily close to 1 for the case of a single task and close to n if it is applied independently to schedule many tasks, which is asymptotically optimal for the natural class of anonymous, task-independent algorithms. Previous work considers the constraint of truthfulness and proves a tight approximation ratio of (n+1)/2 for one task which generalizes to n(n+1)/2 for many tasks. Furthermore, we revisit the truthfulness case and reduce the latter approximation ratio for many tasks down to n, asymptotically matching the best known lower bound. This is done via a detour to the relaxed, fractional version of the problem, for which we are also able to provide an optimal approximation ratio of 1. Finally, we mention that all our algorithms achieve optimal ratios of 1 for the social welfare objective
Strategyproof Facility Location in Perturbation Stable Instances
We consider -Facility Location games, where strategic agents report
their locations on the real line, and a mechanism maps them to
facilities. Each agent seeks to minimize her distance to the nearest facility.
We are interested in (deterministic or randomized) strategyproof mechanisms
without payments that achieve a reasonable approximation ratio to the optimal
social cost of the agents. To circumvent the inapproximability of -Facility
Location by deterministic strategyproof mechanisms, we restrict our attention
to perturbation stable instances. An instance of -Facility Location on the
line is -perturbation stable (or simply, -stable), for some
, if the optimal agent clustering is not affected by moving any
subset of consecutive agent locations closer to each other by a factor at most
. We show that the optimal solution is strategyproof in
-stable instances whose optimal solution does not include any
singleton clusters, and that allocating the facility to the agent next to the
rightmost one in each optimal cluster (or to the unique agent, for singleton
clusters) is strategyproof and -approximate for -stable instances
(even if their optimal solution includes singleton clusters). On the negative
side, we show that for any and any , there is no
deterministic anonymous mechanism that achieves a bounded approximation ratio
and is strategyproof in -stable instances. We also prove
that allocating the facility to a random agent of each optimal cluster is
strategyproof and -approximate in -stable instances. To the best of our
knowledge, this is the first time that the existence of deterministic (resp.
randomized) strategyproof mechanisms with a bounded (resp. constant)
approximation ratio is shown for a large and natural class of -Facility
Location instances