On nash equilibria for a network creation game

Albers, Susanne; Eilts, Stefan; Even-Dar, Eyal; Mansour, Yishay; Roditty, Liam

doi:10.1145/1109557.1109568

Cited by 94 publications

(121 citation statements)

References 8 publications

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“…The lemma exploits that a breadth-first search tree of an equilibrium graph already contains much information about the whole graph. For SUMGAME a similar result with a similar proof is known [1].…”

Section: Bounding the Price Of Anarchy In Maxgamesupporting

confidence: 60%

“…They proved an upper bound O( √ α) on price of anarchy (by showing that price of anarchy is bounded by the diameter of the equilibrium graph), and showed that every Nash equilibrium which is a tree has constant price of anarchy; we will use this result later on. Albers et al [1] showed that price of anarchy is constant for α = O( √ n) (this was also independently and earlier discovered by Lin [15]) and for α ≥ 12n lg n. The latter result is achieved by showing that for α ≥ 12n lg n all Nash equilibria are trees. Albers et al also present a general upper bound 15(1 + (min{α 2 /n, n 2 /α}) 1/3 ) on price of anarchy for all α, which shows that price of anarchy is O(n 1/3 ) for all α. Demaine et al [6] show that price of anarchy is constant already for α = O(n 1−ε ) for any fixed ε ≥ 1/ lg n, and show the general bound 2 O( √ lg n) on price of anarchy for all α. Demaine et al [6] introduced MAXGAME as a natural variant of network creation games, and showed that price of anarchy of MAXGAME is at most 2 for α ≥ n, O(min{4…”

Section: Related Workmentioning

confidence: 61%

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The Price of Anarchy in Network Creation Games Is (Mostly) Constant

Mihaľák

Schlegel

2010

Algorithmic Game Theory

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We study the price of anarchy and the structure of equilibria in network creation games. A network creation game is played by n players {1, 2, . . . , n}, each identified with a vertex of a graph (network), where the strategy of player i, i = 1, . . . , n, is to build some edges adjacent to i. The cost of building an edge is α > 0, a fixed parameter of the game. The goal of every player is to minimize its creation cost plus its usage cost. The creation cost of player i is α times the number of built edges. In the SUMGAME variant, the usage cost of player i is the sum of distances from i to every node of the resulting graph. In the MAXGAME variant, the usage cost is the eccentricity of i in the resulting graph of the game. In this paper we improve previously known bounds on the price of anarchy of the game (of both variants) for various ranges of α, and give new insights into the structure of equilibria for various values of α. The two main results of the paper show that for α > 273 · n all equilibria in SUMGAME are trees and thus the price of anarchy is constant, and that for α > 129 all equilibria in MAXGAME are trees and the price of anarchy is constant. For SUMGAME this answers (almost completely) one of the fundamental open problems in the field-is price of anarchy of the network creation game constant for all values of α?-in an affirmative way, up to a tiny range of α.

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Section: Bounding the Price Of Anarchy In Maxgamesupporting

confidence: 60%

Section: Related Workmentioning

confidence: 61%

The Price of Anarchy in Network Creation Games Is (Mostly) Constant

Mihaľák

Schlegel

2010

Algorithmic Game Theory

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“…This problem has been considered in selfish agent networks [1,[4][5][6], where every node simultaneously tries to solve the single-source problem. Agents have high incentive to join social networks with low diameter because messages spread in short time with small delays.…”

Section: Introductionmentioning

confidence: 99%

Minimizing the Diameter of a Network Using Shortcut Edges

Demaine

Zadimoghaddam

2010

Lecture Notes in Computer Science

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Abstract. We study the problem of minimizing the diameter of a graph by adding k shortcut edges, for speeding up communication in an existing network design. We develop constant-factor approximation algorithms for different variations of this problem. We also show how to improve the approximation ratios using resource augmentation to allow more than k shortcut edges. We observe a close relation between the single-source version of the problem, where we want to minimize the largest distance from a given source vertex, and the well-known k-median problem. First we show that our constant-factor approximation algorithms for the general case solve the single-source problem within a constant factor. Then, using a linear-programming formulation for the single-source version, we find a (1 + ε)-approximation using O(k log n) shortcut edges. To show the tightness of our result, we prove that any ( 3 2 − ε)-approximation for the single-source version must use Ω(k log n) shortcut edges assuming P = NP.

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“…They studied the structure of Nash Equilibria, and conjectured that only trees can be stable graphs in this model. Later, Abers et al came up with an interesting class of stable graphs, and disproved the tree conjecture [1]. They also presented better upper bounds on the price of anarchy.…”

Section: Introductionmentioning

confidence: 99%

Constant Price of Anarchy in Network-Creation Games via Public-Service Advertising

Demaine¹,

Zadimoghaddam²

2012

Internet Mathematics

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Abstract. Network creation games have been studied in many different settings recently. These games are motivated by social networks in which selfish agents want to construct a connection graph among themselves. Each node wants to minimize its average or maximum distance to the others, without paying much to construct the network. Many generalizations have been considered, including non-uniform interests between nodes, general graphs of allowable edges, bounded budget agents, etc. In all of these settings, there is no known constant bound on the price of anarchy. In fact, in many cases, the price of anarchy can be very large, namely, a constant power of the number of agents. This means that we have no control on the behavior of network when agents act selfishly. On the other hand, the price of stability in all these models is constant, which means that there is chance that agents act selfishly and we end up with a reasonable social cost. In this paper, we show how to use an advertising campaign (as introduced in SODA 2009 [2]) to find such efficient equilibria. More formally, we present advertising strategies such that, if an α fraction of the agents agree to cooperate in the campaign, the social cost would be at most O(1/α) times the optimum cost. This is the first constant bound on the price of anarchy that interestingly can be adapted to different settings. We also generalize our method to work in cases that α is not known in advance. Also, we do not need to assume that the cooperating agents spend all their budget in the campaign; even a small fraction (β fraction) would give us a constant price of anarchy.

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On nash equilibria for a network creation game

Cited by 94 publications

References 8 publications

The Price of Anarchy in Network Creation Games Is (Mostly) Constant

The Price of Anarchy in Network Creation Games Is (Mostly) Constant

Minimizing the Diameter of a Network Using Shortcut Edges

Constant Price of Anarchy in Network-Creation Games via Public-Service Advertising

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