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217
Selfish Routing In Capacitated Networks
 MATHEMATICS OF OPERATIONS RESEARCH
, 2003
"... According to Wardrop's first principle, agents in a congested network choose their routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying noncooperative game. A Nash equilibrium does not optimize any global criterion per se, and so there is no apparent reason wh ..."
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Cited by 100 (6 self)
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According to Wardrop's first principle, agents in a congested network choose their routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying noncooperative game. A Nash equilibrium does not optimize any global criterion per se, and so there is no apparent reason why it should be close to a solution of minimal total travel time, i.e. the system optimum. In this paper, we offer extensions of recent positive results on the efficiency of Nash equilibria in traffic networks. In contrast to prior work, we present results for networks with capacities and for latency functions that are nonconvex, nondifferentiable and even discontinuous. The inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows. In this more general model, multiple Nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient. Nonetheless, our main result shows that the best equilibrium is as efficient as in the model without capacities. Moreover, this holds true for broader classes of travel cost functions than considered hitherto.
Bounding the Inefficiency of Equilibria in Nonatomic Congestion Games
 GAMES AND ECONOMIC BEHAVIOR
, 2002
"... Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a "best possible" outcome. We study a nonatomic version of the congestion games ..."
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Cited by 86 (10 self)
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Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a "best possible" outcome. We study a nonatomic version of the congestion games defined by Rosenthal [15], and identify games in which equilibria are approximately optimal in the sense that no other outcome achieves a significantly larger total payoff to the players  games in which optimization by individuals approximately optimizes the social good, in spite of the lack of coordination between players. Our results extend previous work on traffic routing games [16, 17, 18].
The price of being nearsighted
 In SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
, 2006
"... Achieving a global goal based on local information is challenging, especially in complex and largescale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible tradeoff between the amount of local information and the quality o ..."
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Cited by 84 (12 self)
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Achieving a global goal based on local information is challenging, especially in complex and largescale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible tradeoff between the amount of local information and the quality of the global solution for general covering and packing problems. Specifically, we give a distributed algorithm using only small messages which obtains an (ρ∆) 1/kapproximation for general covering and packing problems in time O(k 2), where ρ depends on the LP’s coefficients. If message size is unbounded, we present a second algorithm that achieves an O(n 1/k) approximation in O(k) rounds. Finally, we prove that these algorithms are close to optimal by giving a lower bound on the approximability of packing problems given that each node has to base its decision on information from its kneighborhood. 1
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 ..."
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Cited by 82 (10 self)
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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.
Selfish Traffic Allocation for Server Farms
, 2003
"... We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price... ..."
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Cited by 76 (5 self)
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We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price...
How Much Can Taxes Help Selfish Routing?
 EC'03
, 2003
"... ... in networks. We consider a model of selfish routing in which the latency experienced by network tra#c on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route tra#c on minimumlatency paths. The quality of a routing of tra#c is historically ..."
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Cited by 76 (6 self)
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... in networks. We consider a model of selfish routing in which the latency experienced by network tra#c on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route tra#c on minimumlatency paths. The quality of a routing of tra#c is historically measured by the sum of all travel times, also called the total latency. It is well known
The price of selfish behavior in bilateral network formation
 In Proceedings of the twentyfourth annual ACM symposium on Principles of distributed computing
, 2005
"... Given a collection of selfish agents who wish to establish links to route traffic among themselves, the set of equilibrium network topologies may appear quite different from the centrally enforced optimum. We study the quality (price of anarchy) of equilibrium networks in a game where links require ..."
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Cited by 75 (0 self)
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Given a collection of selfish agents who wish to establish links to route traffic among themselves, the set of equilibrium network topologies may appear quite different from the centrally enforced optimum. We study the quality (price of anarchy) of equilibrium networks in a game where links require the consent of both participants and are negotiated bilaterally, and compare these networks to those generated by an earlier model due to Fabrikant et al. [10] in which links are formed unilaterally. We provide a partial characterization of stable and efficient networks in the bilateral network formation game, and provide examples of stable networks that are not Nash graphs in the unilateral game. We develop an upper and lower bound on the price of anarchy of the bilateral game. An empirical analysis demonstrates that the average price of anarchy is better in the bilateral connection game
Selfish Load Balancing and Atomic Congestion Games
, 2007
"... We revisit a classical load balancing problem in the modern context of decentralized systems and selfinterested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client has a unitlength job and selfishly wants to minimize its own late ..."
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Cited by 72 (3 self)
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We revisit a classical load balancing problem in the modern context of decentralized systems and selfinterested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client has a unitlength job and selfishly wants to minimize its own latency (job completion time). A server’s latency is inversely proportional to its speed, but it grows linearly with (or, more generally, as the pth power of) the number of clients matched to it. This interaction is naturally modeled as an atomic congestion game, which we call selfish load balancing. We analyze the Nash equilibria of this game and prove nearly tight bounds on the price of anarchy (worstcase ratio between a Nash solution and the social optimum). In particular, for linear latency functions, we show that if the server speeds are relatively bounded and the number of clients is large compared with the number of servers, then every Nash assignment approaches social optimum. Without any assumptions on the number of clients, servers, and server speeds, the price of anarchy is at most 2.5. If all servers have the same speed, then the price of anarchy further improves to 1 + 2 / √ 3 ≈ 2.15. We also exhibit a lower bound of 2.01. Our proof techniques can also be adapted for the coordinated load balancing problem under L2 norm, where it slightly improves the best previously known upper bound on the competitive ratio of a simple greedy scheme.
On the price of anarchy and stability of correlated equilibria of linear congestion games
, 2005
"... ..."
Joint Strategy Fictitious Play with Inertia for Potential Games
, 2005
"... We consider finite multiplayer repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these “largescale” games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players ..."
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Cited by 58 (22 self)
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We consider finite multiplayer repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these “largescale” games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in largescale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. A motivating example is a congestion game in a complex transportation system, in which a large number of vehicles make daily routing decisions to optimize their own objectives in response to their observations. In this setting, observing and responding to the individual actions of all vehicles on a daily basis would be a formidable task for any individual driver. This disqualifies some of the well known decision making models such as “Fictitious Play” (FP) as