The Structure and Complexity of Nash Equilibria for a Selfish Routing Game

Fotakis, Dimitris; Kontogiannis, Spyros; Koutsoupias, Elias; Mavronicolas, Marios; Spirakis, Paul G.

doi:10.1007/3-540-45465-9_12

Cited by 180 publications

(183 citation statements)

References 10 publications

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“…As mentioned in Corollary 3.1, the construction of the Monotonicity Lemma (Lemma 3.3) is even valid for singleton games, establishing that every set of continuous cost functions that is consistent for singleton games may only contain monotonic functions. It is well known that singleton congestion games with weighted players and either only nondecreasing or only nonincreasing cost functions admit a PNE; see Even-Dar et al [14], Fotakis et al [15], and Rozenfeld and Tennenholtz [36]. Since the positive result for nondecreasing costs is established via a potential function, these games also possess the FIP.…”

Section: Lemma 64 (Extended Monotonicity Lemma For Undirected Networmentioning

confidence: 99%

“…Dunkel and Schulz [13] showed that it is strongly NP-hard to decide whether or not a weighted congestion game with nonlinear cost functions possesses a PNE. If the strategy of every player contains a single facility only (singleton games), Fotakis et al [15] showed the existence of PNE for linear cost functions (without a constant). Even-Dar et al [14] derived the existence of PNE for load balancing games on parallel unrelated machines.…”

Section: Related Workmentioning

confidence: 99%

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On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Harks

Klimm

2010

Automata, Languages and Programming

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We study the existence of pure Nash equilibria in weighted congestion games. Let denote a set of cost functions. We say that is consistent if every weighted congestion game with cost functions in possesses a pure Nash equilibrium. Our main contribution is a complete characterization of consistency of continuous cost functions. We prove that a set of continuous functions is consistent for two-player games if and only if contains only monotonic functions and for all nonconstant functions c 1 c 2 ∈ , there are constants a b ∈ such that c 1 x = a c 2 x + b for all x ∈ ≥0 . For games with at least three players, we prove that is consistent if and only if exactly one of the following cases holds: (a) contains only affine functions; (b) contains only exponential functions such that c x = a c e x + b c for some a c b c ∈ , where a c and b c may depend on c, while must be equal for every c ∈ . The latter characterization is even valid for three-player games. Finally, we derive several characterizations of consistency of cost functions for games with restricted strategy spaces, such as weighted network congestion games or weighted congestion games with singleton strategies.

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Section: Lemma 64 (Extended Monotonicity Lemma For Undirected Networmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Harks

Klimm

2010

Automata, Languages and Programming

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“…An important subclass of congestion games is the class of singleton congestion games (also known as parallel-link games) in which every player's strategy consists of a single resource [1,11,13,15,16,21,29].…”

Section: Congestion Models and Gamesmentioning

confidence: 99%

“…Such games, also known as parallel-link games, are very well studied in the literature of congestion problems [1,11,13,15,16,21]. We point out to the fact that the parallel-link network topology has received increasing attention in recent years in the context of QoS and the related implementation of priority policies in data networking [25,35,38].…”

Section: Related Workmentioning

confidence: 99%

Congestion Games with Capacitated Resources

Gourvès

Monnot

Moretti

et al. 2012

Algorithmic Game Theory

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Abstract. The players of a congestion game interact by allocating bundles of resources from a common pool. This type of games leads to well studied models for analyzing strategic situations, including networks operated by uncoordinated selfish users. Congestion games constitute a subclass of potential games, meaning that a pure Nash equilibrium emerges from a myopic process where the players iteratively react by switching to a strategy that diminishes their individual cost. With the aim of covering more applications, for instance in communication networks, we extend congestion games to the setting where every resource is endowed with a capacity which possibly limits its number of users. From the negative side, we show that a pure Nash equilibrium is not guaranteed to exist in any case and we prove that deciding whether a game possesses a pure Nash equilibrium is NP-complete. Our positive results state that congestion games with capacities are potential games in the well studied singleton case. Polynomial algorithms that compute these equilibria are also provided.

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“…The former approach assumes that the cost of a resource is some non-decreasing function of its load. This literature includes job scheduling and routing models [22,10,20]. In these cases an individual user will attempt to avoid sharing its resource with others as much as possible.…”

Section: Introductionmentioning

confidence: 99%

Convergence of Best-Response Dynamics in Games with Conflicting Congestion Effects

Feldman

Tamir

2012

Lecture Notes in Computer Science

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Abstract. We study the model of resource allocation games with conflicting congestion effects that was introduced by Feldman and Tamir (2012). In this model, an agent's cost consists of its resource's load (which increases with congestion) and its share in the resource's activation cost (which decreases with congestion). The current work studies the convergence rate of best-response dynamics (BRD) in the case of homogeneous agents. Even within this simple setting, interesting phenomena arise. We show that, in contrast to standard congestion games with identical jobs and resources, the convergence rate of BRD under conflicting congestion effects might be super-linear in the number of jobs. Nevertheless, a specific form of BRD is proposed, which is guaranteed to converge in linear time.

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The Structure and Complexity of Nash Equilibria for a Selfish Routing Game

Cited by 180 publications

References 10 publications

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

On the Existence of Pure Nash Equilibria in Weighted Congestion Games

Congestion Games with Capacitated Resources

Convergence of Best-Response Dynamics in Games with Conflicting Congestion Effects

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