On Strong Equilibria and Improvement Dynamics in Network Creation Games

Janus, Tomasz; Keijzer, Bart de

doi:10.1007/978-3-319-71924-5_12

Cited by 3 publications

(2 citation statements)

References 26 publications

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“…Another research direction would be to consider the unilateral variant of the SDNCG. While this no longer realistically models the formation of social networks, it might still yield interesting insights and it allows for studying stronger solution concepts like the Nash equilibrium or strong Nash equilibria, similar to [48,49]. Also, altering the utility function, e.g., to using the maximum distance instead of the summed distances, or the probability of infection, similar to [38], seems promising.…”

Section: Discussionmentioning

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: Discussionmentioning

confidence: 99%

Social Distancing Network Creation

et al. 2023

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“…Another research direction would be to consider the unilateral variant of the SDNCG. While this no longer realistically models the formation of social networks, it might still yield interesting insights and it allows for studying stronger solution concepts like the Nash equilibrium or strong Nash equilibria, similar to [33,6]. Also, altering the utility function, e.g., to using the maximum distance instead of the summed distances, or the probability of infection, similar to [13], seems promising.…”

Section: Discussionmentioning

confidence: 99%

Social Distancing Network Creation

Friedrich¹,

Gawendowicz²,

Lenzner³

et al. 2022

Preprint

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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. [PODC 2003] where agents aim at being as central as possible in the created network. Thus, our work is in-line with studies that compare minimization problems with their maximization versions.We look at two variants of network creation governed by social distancing. In the first variant, there are no restrictions on the connections being formed. We characterize optimal and equilibrium networks, and we derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant is the model's generalization that allows restrictions on the connections that can be formed. 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, compared the well-studied inverse models, under social distancing the agents' selfish behavior has a significantly stronger impact on the quality of the equilibria, i.e., allowing socially much worse stable states.

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On the Tree Conjecture for the Network Creation Game

Bilò

Lenzner

2019

Theory Comput Syst

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Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. [PODC'03] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of α per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all α and that for α ≥ n all equilibrium networks are trees.We introduce a novel technique for analyzing stable networks for high edge-price α and employ it to improve on the best known bounds for both conjectures. In particular we show that for α > 4n − 13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of α. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.

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On Strong Equilibria and Improvement Dynamics in Network Creation Games

Cited by 3 publications

References 26 publications

Social Distancing Network Creation

Social Distancing Network Creation

Social Distancing Network Creation

On the Tree Conjecture for the Network Creation Game

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