On the Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games,,

Christodoulou, George; Koutsoupias, Elias

doi:10.1007/11561071_8

Cited by 124 publications

(120 citation statements)

References 30 publications

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“…Congestion games nicely model situations that arise in selfish routing, resource allocation and network design problems, and the PoA for these games is now quite well-understood [16,7,6,3]. By comparison, much less work has been done on the PoS: The PoS for network design games has been studied by [2,5,1,9,11], while the PoS for routing games 1 was studied by [2,6,4].…”

Section: Introductionmentioning

confidence: 99%

On the Price of Stability for Undirected Network Design

Christodoulou

Chung

Ligett

et al. 2010

Approximation and Online Algorithms

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We continue the study of the effects of selfish behavior in the network design problem. We provide new bounds for the price of stability for network design with fair cost allocation for undirected graphs. We consider the most general case, for which the best known upper bound is the Harmonic number H n , where n is the number of agents, and the best previously known lower bound is 12/7 ≈ 1.778.We present a nontrivial lower bound of 42/23 ≈ 1.8261. Furthermore, we show that for two players, the price of stability is exactly 4/3, while for three players it is at least 74/48 ≈ 1.542 and at most 1.65. These are the first improvements on the bound of H n for general networks. In particular, this demonstrates a separation between the price of stability on undirected graphs and that on directed graphs, where H n is tight. Previously, such a gap was only known for the cases where all players have a shared source, and for weighted players.Keywords Algorithmic Game Theory ⋅ Price of Stability ⋅ Network Design A preliminary version of this work appeared in [8].

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Section: Introductionmentioning

confidence: 99%

On the Price of Stability for Undirected Network Design

Christodoulou

Chung

Ligett

et al. 2010

Approximation and Online Algorithms

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“…The main focus was latency minimization for linear and polynomial latency functions [3,5,9]. The price of stability for linear latency functions has been studied by Christodoulou and Koutsoupias [4].…”

Section: Introductionmentioning

confidence: 99%

On the Price of Stability for Designing Undirected Networks with Fair Cost Allocations

Fiat

Kaplan

Levy

et al. 2006

Automata, Languages and Programming

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Abstract. In this paper we address the open problem of bounding the price of stability for network design with fair cost allocation for undirected graphs posed in [1]. We consider the case where there is an agent in every vertex. We show that the price of stability is O(log log n). We prove this by defining a particular improving dynamics in a related graph. This proof technique may have other applications and is of independent interest.

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“…[28]). In the atomic setting, Christodoulou and Koutsoupias [10] proved that the PoS of congestion games with affine latencies lies between 1+ √ 3/3 and 1.6. Subsequently, Caragiannis et al [7,Theorem 6] proved that the PoS of affine congestion games is 1 + √ 3/3, and that for non-symmetric singleton games with latency functions in class D, the PoS is at most ρ(D).…”

Section: √ 3 23mentioning

confidence: 99%

“…[22,23,17,6,9,10,4,7]), and bounding the convergence time to pure Nash equilibria if the players select their strategies in a selfish and decentralized fashion (see e.g. [14,21,1,8]).…”

Section: Introductionmentioning

confidence: 99%

Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy

Fotakis¹

2008

Algorithmic Game Theory

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Abstract. We investigate the effect of linear independence in the strategies of congestion games on the convergence time of best improvement sequences and on the pure Price of Anarchy. In particular, we consider symmetric congestion games on extension-parallel networks, an interesting class of networks with linearly independent paths, and establish two remarkable properties previously known only for parallel-link games. More precisely, we show that for arbitrary (non-negative and non-decreasing) latency functions, any best improvement sequence reaches a pure Nash equilibrium in at most as many steps as the number of players, and that for latency functions in class D, the pure Price of Anarchy is at most ρ(D). As a by-product of our analysis, we obtain that for symmetric congestion games on general networks with latency functions in class D, the Price of Stability is at most ρ(D).

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On the Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games,,

Cited by 124 publications

References 30 publications

On the Price of Stability for Undirected Network Design

On the Price of Stability for Undirected Network Design

On the Price of Stability for Designing Undirected Networks with Fair Cost Allocations

Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy

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