On the Tree Conjecture for the Network Creation Game

Abstract

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. (2003) 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 αn 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 bound for the latter conjecture. 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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Notes

  1. 1.

    No edge can have two owners in any equilibrium network. Hence, we will assume throughout the paper that each edge in E(s) has a unique owner.

  2. 2.

    A swap of edge (a, b) to edge (a, c) by agent a who owns edge (a, b) consists of deleting edge (a, b) and buying edge (a, c).

  3. 3.

    In a cycle of length , two vertices of the cycle are antipodal if their distance is ⌊/2⌋.

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Correspondence to Davide Bilò.

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This article is part of the Topical Collection on Special Issue on Theoretical Aspects of Computer Science (2018)

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Bilò, D., Lenzner, P. On the Tree Conjecture for the Network Creation Game. Theory Comput Syst 64, 422–443 (2020). https://doi.org/10.1007/s00224-019-09945-9

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Keywords

  • Network creation games
  • Price of anarchy
  • Tree conjecture
  • Algorithmic game theory