4,832 research outputs found
Load Balancing Congestion Games and their Asymptotic Behavior
A central question in routing games has been to establish conditions for the
uniqueness of the equilibrium, either in terms of network topology or in terms
of costs. This question is well understood in two classes of routing games. The
first is the non-atomic routing introduced by Wardrop on 1952 in the context of
road traffic in which each player (car) is infinitesimally small; a single car
has a negligible impact on the congestion. Each car wishes to minimize its
expected delay. Under arbitrary topology, such games are known to have a convex
potential and thus a unique equilibrium. The second framework is splitable
atomic games: there are finitely many players, each controlling the route of a
population of individuals (let them be cars in road traffic or packets in the
communication networks). In this paper, we study two other frameworks of
routing games in which each of several players has an integer number of
connections (which are population of packets) to route and where there is a
constraint that a connection cannot be split. Through a particular game with a
simple three link topology, we identify various novel and surprising properties
of games within these frameworks. We show in particular that equilibria are non
unique even in the potential game setting of Rosenthal with strictly convex
link costs. We further show that non-symmetric equilibria arise in symmetric
networks. I. INTRODUCTION A central question in routing games has been to
establish conditions for the uniqueness of the equilibria, either in terms of
the network topology or in terms of the costs. A survey on these issues is
given in [1]. The question of uniqueness of equilibria has been studied in two
different frameworks. The first, which we call F1, is the non-atomic routing
introduced by Wardrop on 1952 in the context of road traffic in which each
player (car) is infinitesimally small; a single car has a negligible impact on
the congestion. Each car wishes to minimize its expected delay. Under arbitrary
topology, such games are known to have a convex potential and thus have a
unique equilibrium [2]. The second framework, denoted by F2, is splitable
atomic games. There are finitely many players, each controlling the route of a
population of individuals. This type of games have already been studied in the
context of road traffic by Haurie and Marcotte [3] but have become central in
the telecom community to model routing decisions of Internet Service Providers
that can decide how to split the traffic of their subscribers among various
routes so as to minimize network congestion [4]. In this paper we study
properties of equilibria in two other frameworks of routing games which exhibit
surprisin
Path deviations outperform approximate stability in heterogeneous congestion games
We consider non-atomic network congestion games with heterogeneous players
where the latencies of the paths are subject to some bounded deviations. This
model encompasses several well-studied extensions of the classical Wardrop
model which incorporate, for example, risk-aversion, altruism or travel time
delays. Our main goal is to analyze the worst-case deterioration in social cost
of a perturbed Nash flow (i.e., for the perturbed latencies) with respect to an
original Nash flow. We show that for homogeneous players perturbed Nash flows
coincide with approximate Nash flows and derive tight bounds on their
inefficiency. In contrast, we show that for heterogeneous populations this
equivalence does not hold. We derive tight bounds on the inefficiency of both
perturbed and approximate Nash flows for arbitrary player sensitivity
distributions. Intuitively, our results suggest that the negative impact of
path deviations (e.g., caused by risk-averse behavior or latency perturbations)
is less severe than approximate stability (e.g., caused by limited
responsiveness or bounded rationality). We also obtain a tight bound on the
inefficiency of perturbed Nash flows for matroid congestion games and
homogeneous populations if the path deviations can be decomposed into edge
deviations. In particular, this provides a tight bound on the Price of
Risk-Aversion for matroid congestion games
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
Bottleneck Routing Games with Low Price of Anarchy
We study {\em bottleneck routing games} where the social cost is determined
by the worst congestion on any edge in the network. In the literature,
bottleneck games assume player utility costs determined by the worst congested
edge in their paths. However, the Nash equilibria of such games are inefficient
since the price of anarchy can be very high and proportional to the size of the
network. In order to obtain smaller price of anarchy we introduce {\em
exponential bottleneck games} where the utility costs of the players are
exponential functions of their congestions. We find that exponential bottleneck
games are very efficient and give a poly-log bound on the price of anarchy:
, where is the largest path length in the
players' strategy sets and is the set of edges in the graph. By adjusting
the exponential utility costs with a logarithm we obtain games whose player
costs are almost identical to those in regular bottleneck games, and at the
same time have the good price of anarchy of exponential games.Comment: 12 page
Atomic Routing Games on Maximum Congestion
We study atomic routing congestion games in which each player chooses a path in the network from its strategy set (a collection of paths) with the objective to minimize the maximum congestion along any edge on its selected path. The social cost is the global maximum congestion on any edge in the network. We show that for arbitrary routing games, the price of stability is 1, and the price of anarchy, PoA, is bounded by Îș â 1 †PoA †c(Îș 2 + log 2 n), where Îș is the length of the longest cycle in the network, n is the size of the network and c is a constant. Further, any best response dynamic converges to a Nash equilibrium. Our bounds show that for maximum congestion games, the topology of the network, in particular the length of cycles, plays an important role in determining the quality of the Nash equilibria. A fundamental issue in the management of large scale communication networks is to route the packet traffic so as to optimize the network performance. Our measure of network performance is the worst bottleneck (most used link) in the system. The model we use for network traffic is that of finite, unsplittable packets (atomic flow), and each packetâs path is controlled independentl
- âŠ