8,560 research outputs found
Smoothed Performance Guarantees for Local Search
We study popular local search and greedy algorithms for scheduling. The
performance guarantee of these algorithms is well understood, but the
worst-case lower bounds seem somewhat contrived and it is questionable if they
arise in practical applications. To find out how robust these bounds are, we
study the algorithms in the framework of smoothed analysis, in which instances
are subject to some degree of random noise.
While the lower bounds for all scheduling variants with restricted machines
are rather robust, we find out that the bounds are fragile for unrestricted
machines. In particular, we show that the smoothed performance guarantee of the
jump and the lex-jump algorithm are (in contrast to the worst case) independent
of the number of machines. They are Theta(phi) and Theta(log(phi)),
respectively, where 1/phi is a parameter measuring the magnitude of the
perturbation. The latter immediately implies that also the smoothed price of
anarchy is Theta(log(phi)) for routing games on parallel links. Additionally we
show that for unrestricted machines also the greedy list scheduling algorithm
has an approximation guarantee of Theta(log(phi))
The price of anarchy and stability in general noisy best-response dynamics
Logit-response dynamics (Alos-Ferrer and Netzer, Games and Economic Behavior
2010) are a rich and natural class of noisy best-response dynamics. In this
work we revise the price of anarchy and the price of stability by considering
the quality of long-run equilibria in these dynamics. Our results show that
prior studies on simpler dynamics of this type can strongly depend on a
synchronous schedule of the players' moves. In particular, a small noise by
itself is not enough to improve the quality of equilibria as soon as other very
natural schedules are used
Non-clairvoyant Scheduling Games
In a scheduling game, each player owns a job and chooses a machine to execute
it. While the social cost is the maximal load over all machines (makespan), the
cost (disutility) of each player is the completion time of its own job. In the
game, players may follow selfish strategies to optimize their cost and
therefore their behaviors do not necessarily lead the game to an equilibrium.
Even in the case there is an equilibrium, its makespan might be much larger
than the social optimum, and this inefficiency is measured by the price of
anarchy -- the worst ratio between the makespan of an equilibrium and the
optimum. Coordination mechanisms aim to reduce the price of anarchy by
designing scheduling policies that specify how jobs assigned to a same machine
are to be scheduled. Typically these policies define the schedule according to
the processing times as announced by the jobs. One could wonder if there are
policies that do not require this knowledge, and still provide a good price of
anarchy. This would make the processing times be private information and avoid
the problem of truthfulness. In this paper we study these so-called
non-clairvoyant policies. In particular, we study the RANDOM policy that
schedules the jobs in a random order without preemption, and the EQUI policy
that schedules the jobs in parallel using time-multiplexing, assigning each job
an equal fraction of CPU time
Price of Anarchy in Bernoulli Congestion Games with Affine Costs
We consider an atomic congestion game in which each player participates in
the game with an exogenous and known probability , independently
of everybody else, or stays out and incurs no cost. We first prove that the
resulting game is potential. Then, we compute the parameterized price of
anarchy to characterize the impact of demand uncertainty on the efficiency of
selfish behavior. It turns out that the price of anarchy as a function of the
maximum participation probability is a nondecreasing
function. The worst case is attained when players have the same participation
probabilities . For the case of affine costs, we provide an
analytic expression for the parameterized price of anarchy as a function of
. This function is continuous on , is equal to for , and increases towards when . Our work can be interpreted as
providing a continuous transition between the price of anarchy of nonatomic and
atomic games, which are the extremes of the price of anarchy function we
characterize. We show that these bounds are tight and are attained on routing
games -- as opposed to general congestion games -- with purely linear costs
(i.e., with no constant terms).Comment: 29 pages, 6 figure
How Good is Bargained Routing?
In the context of networking, research has focused on non-cooperative games,
where the selfish agents cannot reach a binding agreement on the way they would
share the infrastructure. Many approaches have been proposed for mitigating the
typically inefficient operating points. However, in a growing number of
networking scenarios selfish agents are able to communicate and reach an
agreement. Hence, the degradation of performance should be considered at an
operating point of a cooperative game. Accordingly, our goal is to lay
foundations for the application of cooperative game theory to fundamental
problems in networking. We explain our choice of the Nash Bargaining Scheme
(NBS) as the solution concept, and introduce the Price of Selfishness (PoS),
which considers the degradation of performance at the worst NBS. We focus on
the fundamental load balancing game of routing over parallel links. First, we
consider agents with identical performance objectives. We show that, while the
PoA here can be large, through bargaining, all agents, and the system, strictly
improve their performance. Interestingly, in a two-agent system or when all
agents have identical demands, we establish that they reach social optimality.
We then consider agents with different performance objectives and demonstrate
that the PoS and PoA can be unbounded, yet we explain why both measures are
unsuitable. Accordingly, we introduce the Price of Heterogeneity (PoH), as an
extension of the PoA. We establish an upper-bound on the PoH and indicate its
further motivation for bargaining. Finally, we discuss network design
guidelines that follow from our finding
Selfish Jobs with Favorite Machines: Price of Anarchy vs Strong Price of Anarchy
We consider the well-studied game-theoretic version of machine scheduling in
which jobs correspond to self-interested users and machines correspond to
resources. Here each user chooses a machine trying to minimize her own cost,
and such selfish behavior typically results in some equilibrium which is not
globally optimal: An equilibrium is an allocation where no user can reduce her
own cost by moving to another machine, which in general need not minimize the
makespan, i.e., the maximum load over the machines.
We provide tight bounds on two well-studied notions in algorithmic game
theory, namely, the price of anarchy and the strong price of anarchy on machine
scheduling setting which lies in between the related and the unrelated machine
case. Both notions study the social cost (makespan) of the worst equilibrium
compared to the optimum, with the strong price of anarchy restricting to a
stronger form of equilibria. Our results extend a prior study comparing the
price of anarchy to the strong price of anarchy for two related machines
(Epstein, Acta Informatica 2010), thus providing further insights on the
relation between these concepts. Our exact bounds give a qualitative and
quantitative comparison between the two models. The bounds also show that the
setting is indeed easier than the two unrelated machines: In the latter, the
strong price of anarchy is , while in ours it is strictly smaller.Comment: Extended abstract to appear in COCOA'1
Unilateral Altruism in Network Routing Games with Atomic Players
We study a routing game in which one of the players unilaterally acts
altruistically by taking into consideration the latency cost of other players
as well as his own. By not playing selfishly, a player can not only improve the
other players' equilibrium utility but also improve his own equilibrium
utility. To quantify the effect, we define a metric called the Value of
Unilateral Altruism (VoU) to be the ratio of the equilibrium utility of the
altruistic user to the equilibrium utility he would have received in Nash
equilibrium if he were selfish. We show by example that the VoU, in a game with
nonlinear latency functions and atomic players, can be arbitrarily large. Since
the Nash equilibrium social welfare of this example is arbitrarily far from
social optimum, this example also has a Price of Anarchy (PoA) that is
unbounded. The example is driven by there being a small number of players since
the same example with non-atomic players yields a Nash equilibrium that is
fully efficient
Pareto-optimal Nash equilibrium in capacity allocation game for self-managed networks
In this paper we introduce a capacity allocation game which models the
problem of maximizing network utility from the perspective of distributed
noncooperative agents. Motivated by the idea of self-managed networks, in the
developed framework decision-making entities are associated with individual
transmission links, deciding on the way they split capacity among concurrent
flows. An efficient decentralized algorithm is given for computing strongly
Pareto-optimal strategies, constituting a pure Nash equilibrium. Subsequently,
we discuss the properties of the introduced game related to the Price of
Anarchy and Price of Stability. The paper is concluded with an experimental
study.Comment: Computer Networks, 201
The Network Improvement Problem for Equilibrium Routing
In routing games, agents pick their routes through a network to minimize
their own delay. A primary concern for the network designer in routing games is
the average agent delay at equilibrium. A number of methods to control this
average delay have received substantial attention, including network tolls,
Stackelberg routing, and edge removal.
A related approach with arguably greater practical relevance is that of
making investments in improvements to the edges of the network, so that, for a
given investment budget, the average delay at equilibrium in the improved
network is minimized. This problem has received considerable attention in the
literature on transportation research and a number of different algorithms have
been studied. To our knowledge, none of this work gives guarantees on the
output quality of any polynomial-time algorithm. We study a model for this
problem introduced in transportation research literature, and present both
hardness results and algorithms that obtain nearly optimal performance
guarantees.
- We first show that a simple algorithm obtains good approximation guarantees
for the problem. Despite its simplicity, we show that for affine delays the
approximation ratio of 4/3 obtained by the algorithm cannot be improved.
- To obtain better results, we then consider restricted topologies. For
graphs consisting of parallel paths with affine delay functions we give an
optimal algorithm. However, for graphs that consist of a series of parallel
links, we show the problem is weakly NP-hard.
- Finally, we consider the problem in series-parallel graphs, and give an
FPTAS for this case.
Our work thus formalizes the intuition held by transportation researchers
that the network improvement problem is hard, and presents topology-dependent
algorithms that have provably tight approximation guarantees.Comment: 27 pages (including abstract), 3 figure
Study of the effect of cost policies in the convergence of selfish strategies in Pure Nash Equilibria in Congestion Games
In this work we study of competitive situations among users of a set of
global resources. More precisely we study the effect of cost policies used by
these resources in the convergence time to a pure Nash equilibrium. The work is
divided in two parts. In the theoretical part we prove lower and upper bounds
on the convergence time for various cost policies. We then implement all the
models we study and provide some experimental results. These results follows
the theoretical with one exception which is the most interesting among the
experiments. In the case of coalitional users the theoretical upper bound is
pseudo-polynomial to the number of users but the experimental results shows
that the convergence time is polynomial.Comment: Extended Abstrac
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