An Improved Bound for the Tree Conjecture in Network Creation Games

Dippel, Jack; Vetta, Adrian

doi:10.48550/arxiv.2106.05175

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…The latter also proved that the PoA is constant for α ∈ O(n 1−ε ) for any fixed ε > 1 log n . For large α, it was shown by Bilò and Lenzner [24] that for α > 4n − 13 all Nash equilibria must be trees and this bound was recently improved by Dippel and Vetta [26] to α > 3n − 3. This implies a constant PoA for α > 3n − 3.…”

Section: Related Workmentioning

confidence: 99%

Social Distancing Network Creation

et al. 2023

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During a pandemic people have to find a trade-off between meeting others and staying safely at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a game-theoretic network creation model in which selfish agents can form bilateral connections. They benefit from network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our model can be seen as the inverse to the well-studied Network Creation Game by Fabrikant et al. (in: PODC 2003, pp 347–351, 2003. https://doi.org/10.1145/872035.872088), where agents aim at being as central as possible in the created network. We look at two variants of network creation governed by social distancing. Firstly, a variant without connection restrictions, where we characterize optimal and equilibrium networks, and derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant allows connection restrictions. As our main result, we prove that Swap-Maximal Routing-Cost Spanning Trees, an efficiently computable weaker variant of Maximum Routing-Cost Spanning Trees, actually resemble equilibria for a significant range of the parameter space. Moreover, we give almost tight bounds on the Price of Anarchy and Price of Stability. These results imply that under social distancing the agents’ selfishness has a strong impact on the quality of the equilibria.

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Section: Related Workmentioning

confidence: 99%

Social Distancing Network Creation

et al. 2023

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“…While the original tree conjecture was disproven [1], it was reformulated to hold for α ≥ n. This is best possible, since non-tree networks in NE exist for α < n [33]. A recent line of research [1,37,33,2,3,5,20] proved the adapted conjecture to hold for α > 3n − 3, further refined the constant upper bounds on the PoA for tree networks, and showed that the PoA is constant if α > n(1 + ε), for any ε > 0. The currently best general bound on the PoA that holds for all α > 0 was established by Demaine et al [19].…”

Section: Related Workmentioning

confidence: 99%

The Impact of Cooperation in Bilateral Network Creation

Friedrich¹,

Gawendowicz²,

Lenzner³

et al. 2022

Preprint

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Many real-world networks, like the Internet, are not the result of central design but instead the outcome of the interaction of local agents who are selfishly optimizing for their individual utility. The famous Network Creation Game [23] enables us to understand such processes, their dynamics, and their outcomes in the form of equilibrium states. In this model, agents buy incident edges towards other agents for a price of α and simultaneously try to minimize their buying cost and their total hop distance. Since in many real-world networks, e.g., social networks, consent from both sides is required to maintain a connection, Corbo and Parkes [14] proposed a bilateral version of the Network Creation Game, in which mutual consent and payment are required in order to create edges. It is known that the bilateral version has a significantly higher Price of Anarchy, compared to the unilateral version. This is counter-intuitive, since cooperation should help to avoid socially bad states. We investigate this phenomenon by analyzing the Price of Anarchy of the bilateral version with respect to different solution concepts that allow for various degrees of cooperation among the agents. With this, we provide insights into what kind of cooperation is needed to ensure that socially good networks are created. We present a collection of asymptotically tight bounds on the Price of Anarchy that precisely map the impact of cooperation on the quality of tree networks and we find that weak forms of cooperation already yield a significantly improved Price of Anarchy. Moreover, for general networks we show that enhanced cooperation yields close to optimal networks for a wide range of edge prices.

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“…A series of works have contributed to this threshold from 12n log n [12] to 273n [3], 65n [13], 17n [14], and to 4n − 13 [9]. Very recently a preprint by Dippel and Vetta [15] claimed an improved bound 3n − 3.…”

Section: Introductionmentioning

confidence: 99%

On Tree Equilibria in Max-Distance Network Creation Games

Wang

2021

Preprint

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We study the Nash equilibrium and the price of anarchy in the max-distance network creation game. The network creation game, first introduced and studied by Fabrikant et al.[1], is a classic model for real-world networks from a game-theoretic point of view. In a network creation game with n selfish vertex agents, each vertex can build undirected edges incident to a subset of the other vertices. The goal of every agent is to minimize its creation cost plus its usage cost, where the creation cost is the unit edge cost α times the number of edges it builds, and the usage cost is the sum of distances to all other agents in the resulting network. The max-distance network creation game, introduced and studied by Demaine et al. [2], is a key variant of the original game, where the usage cost takes into account the maximum distance instead. The main result of this paper shows that for α ≥ 23 all equilibrium graphs in the max-distance network creation game must be trees, while the best bound in previous work is α > 129 [3]. We also improve the constant upper bound on the price of anarchy to 3 for tree equilibria. Our work brings new insights into the structure of Nash equilibria and takes one step forward in settling the so-called tree conjecture in the max-distance network creation game.

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An Improved Bound for the Tree Conjecture in Network Creation Games

Cited by 4 publications

References 13 publications

Social Distancing Network Creation

Social Distancing Network Creation

The Impact of Cooperation in Bilateral Network Creation

On Tree Equilibria in Max-Distance Network Creation Games

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