Results 1  10
of
88
Selfish Unsplittable Flows
 Theoretical Computer Science
, 2004
"... What is the price of anarchy when unsplittable demands are routed selfishly in general networks with loaddependent edge delays? Motivated by this question we generalize the model of [14] to the case of weighted congestion games. We show that varying demands of users crucially affect the nature o ..."
Abstract

Cited by 81 (10 self)
 Add to MetaCart
What is the price of anarchy when unsplittable demands are routed selfishly in general networks with loaddependent edge delays? Motivated by this question we generalize the model of [14] to the case of weighted congestion games. We show that varying demands of users crucially affect the nature of these games, which are no longer isomorphic to exact potential games, even for very simple instances. Indeed we construct examples where even a singlecommodity (weighted) network congestion game may have no pure Nash equilibrium.
On Spectrum Sharing Games
, 2007
"... Efficient spectrumsharing mechanisms are crucial to alleviate the bandwidth limitation in wireless networks. In this paper, we consider the following question: can free spectrum be shared efficiently? We study this problem in the context of 802.11 or WiFi networks. Each access point (AP) in a WiFi ..."
Abstract

Cited by 78 (3 self)
 Add to MetaCart
(Show Context)
Efficient spectrumsharing mechanisms are crucial to alleviate the bandwidth limitation in wireless networks. In this paper, we consider the following question: can free spectrum be shared efficiently? We study this problem in the context of 802.11 or WiFi networks. Each access point (AP) in a WiFi network must be assigned a channel for it to service users. There are only finitely many possible channels that can be assigned. Moreover, neighboring access points must use different channels so as to avoid interference. Currently these channels are assigned by administrators who carefully consider channel conflicts and network loads. Channel conflicts among APs operated by different entities are currently resolved in an ad hoc manner or not resolved at all. We view the channel assignment problem as a game, where the players are the service providers and APs are acquired sequentially. We consider the price of anarchy of this game, which is the ratio between the total coverage of the APs in the worst Nash equilibrium of the game and what the total coverage of the APs would be if the channel assignment were done optimally by a central authority. We provide bounds on the price of anarchy depending on assumptions on the underlying
Convergence to Approximate Nash Equilibria in Congestion Games
 In SODA ’07
, 2007
"... ..."
(Show Context)
Strong Price of Anarchy
"... A strong equilibrium (Aumann 1959) is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy to be the ratio of the worst case strong equilibrium to the social optimum. In contrast to the traditional price of anarchy, which quantifies the loss i ..."
Abstract

Cited by 71 (10 self)
 Add to MetaCart
A strong equilibrium (Aumann 1959) is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy to be the ratio of the worst case strong equilibrium to the social optimum. In contrast to the traditional price of anarchy, which quantifies the loss incurred due to both selfishness and lack of coordination, the strong price of anarchy isolates the loss originated from selfishness from that obtained due to lack of coordination. We study the strong price of anarchy in two settings, one of job scheduling and the other of network creation. In the job scheduling game we show that for unrelated machines the strong price of anarchy can be bounded as a function of the number of machines and the size of the coalition. For the network creation game we show that the strong price of anarchy is at most 2. In both cases we show that a strong
Routing without regret: On convergence to nash equilibria of regretminimizing algorithms in routing games
 In PODC
, 2006
"... Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging envi ..."
Abstract

Cited by 58 (7 self)
 Add to MetaCart
(Show Context)
Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging environments. There has also been substantial work on analyzing properties of Nash equilibria in routing games. In this paper, we consider the question: if each player in a routing game uses a noregret strategy, will behavior converge to a Nash equilibrium? In general games the answer to this question is known to be no in a strong sense, but routing games havesubstantially more structure. In this paper we show that in the Wardrop setting of multicommodity flow and infinitesimalagents, behavior will approach Nash equilibrium (formally, on most days, the cost of the flow will be close to the cost of the cheapest paths possible given that flow) at a rate that dependspolynomially on the players ' regret bounds and the maximum slope of any latency function. We also show that priceofanarchy results may be applied to these approximate equilibria, and alsoconsider the finitesize (noninfinitesimal) loadbalancing model of Azar [2].
Computing Equilibria in MultiPlayer Games
 In Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2004
"... We initiate the systematic study of algorithmic issues involved in finding equilibria (Nash and correlated) in games with a large number of players; such games, in order to be computationally meaningful, must be presented in some succinct, gamespecific way. We develop a general framework for obta ..."
Abstract

Cited by 53 (4 self)
 Add to MetaCart
(Show Context)
We initiate the systematic study of algorithmic issues involved in finding equilibria (Nash and correlated) in games with a large number of players; such games, in order to be computationally meaningful, must be presented in some succinct, gamespecific way. We develop a general framework for obtaining polynomialtime algorithms for optimizing over correlated equilibria in such settings, and show how it can be applied successfully to symmetric games (for which we actually find an exact polytopal characterization), graphical games, and congestion games, among others. We also present complexity results implying that such algorithms are not possible in certain other such games. Finally, we present a polynomialtime algorithm, based on quantifier elimination, for finding a Nash equilibrium in symmetric games when the number of strategies is relatively small.
A New Model for Selfish Routing
 Proceedings of the 21st International Symposium on Theoretical Aspects of Computer Science (STACS’04), LNCS 2996
, 2004
"... Abstract. In this work, we introduce and study a new model for selfish routing over noncooperative networks that combines features from the two such best studied models, namely the KP model and the Wardrop model in an interesting way. We consider a set of n users, each using a mixed strategy to shi ..."
Abstract

Cited by 51 (8 self)
 Add to MetaCart
(Show Context)
Abstract. In this work, we introduce and study a new model for selfish routing over noncooperative networks that combines features from the two such best studied models, namely the KP model and the Wardrop model in an interesting way. We consider a set of n users, each using a mixed strategy to ship its unsplittable traffic over a network consisting of m parallel links. In a Nash equilibrium, no user can increase its Individual Cost by unilaterally deviating from its strategy. To evaluate the performance of such Nash equilibria, we introduce Quadratic Social Cost as a certain sum of Individual Costs – namely, the sum of the expectations of the squares of the incurred link latencies. This definition is unlike the KP model, where Maximum Social Cost has been defined as the maximum of Individual Costs. We analyse the impact of our modeling assumptions on the computation of Quadratic Social Cost, on the structure of worstcase Nash equilibria, and on bounds on the Quadratic Coordination Ratio.
Convergence issues in competitive games
 In APPROXRANDOM
, 2004
"... 3 that of optimal. For nplayer validutility games, in general, after one round we obtain a 1 2napproximate solution. For market sharing games we prove that one round of selfish response behavior of playersgives \Omega ( ..."
Abstract

Cited by 47 (9 self)
 Add to MetaCart
(Show Context)
3 that of optimal. For nplayer validutility games, in general, after one round we obtain a 1 2napproximate solution. For market sharing games we prove that one round of selfish response behavior of playersgives \Omega (
Coordination Mechanisms for Selfish Scheduling
, 2006
"... In machine scheduling, a set of jobs must be scheduled on a set of machines so as to minimize some global objective function, such as the makespan considered in this paper. In practice, jobs are often controlled by independent, selfishly acting agents, each of which selects a machine for processing ..."
Abstract

Cited by 46 (6 self)
 Add to MetaCart
(Show Context)
In machine scheduling, a set of jobs must be scheduled on a set of machines so as to minimize some global objective function, such as the makespan considered in this paper. In practice, jobs are often controlled by independent, selfishly acting agents, each of which selects a machine for processing that minimizes the (expected) completion time of its job. This scenario can be formalized as a game in which the players are job owners, the strategies are machines, and the disutility to each player in a strategy profile is the completion time of its job in the corresponding schedule. The equilibria of these games may result in largerthanoptimal overall makespan. The price of anarchy is the ratio of the worstcase equilibrium makespan to the optimal makespan. In this paper, we design and analyze scheduling policies, or coordination mechanisms, for machines which aim to minimize the price of anarchy (restricted to pure Nash equilibria) of the corresponding game. We study coordination mechanisms for four classes of multiprocessor machine scheduling problems and derive upper and lower bounds for the price of anarchy of these mechanisms. For several of the proposed mechanisms, we are also able to prove that the system converges to a purestrategy Nash equilibrium in a linear number of rounds. Finally, we note that our results are applicable to several practical problems arising in communication networks.
Distributed selfish load balancing
, 2006
"... Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A gametheoretic mechanism to find a suitable allocation is to associate each task with a “selfish agent”, and require each agent to select a resource, with the cost of a resource being the number of ..."
Abstract

Cited by 39 (2 self)
 Add to MetaCart
(Show Context)
Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A gametheoretic mechanism to find a suitable allocation is to associate each task with a “selfish agent”, and require each agent to select a resource, with the cost of a resource being the number of agents to select it. Agents would then be expected to migrate from overloaded to underloaded resources, until the allocation becomes balanced. Recent work has studied the question of how this can take place within a distributed setting in which agents migrate selfishly without any centralized control. In this paper we discuss a natural protocol for the agents which combines the following desirable features: It can be implemented in a strongly distributed setting, uses no central control, and has good convergence properties. For m ≫ n, the system becomes approximately balanced (an ǫNash equilibrium) in expected time O(log log m). We show using a martingale technique that the process converges to a perfectly balanced allocation in expected time O(log log m + n 4). We also give a lower bound of Ω(max{loglog m, n}) for the convergence time.