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On the Tree Conjecture for the Network Creation Game

  • Davide BilòEmail author
  • Pascal Lenzner
Article
Part of the following topical collections:
  1. Special Issue on Theoretical Aspects of Computer Science (2018)

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.

Keywords

Network creation games Price of anarchy Tree conjecture Algorithmic game theory 

Notes

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Authors and Affiliations

  1. 1.Department of Humanities and Social SciencesUniversity of SassariSassariItaly
  2. 2.Algorithm Engineering Group, Hasso Plattner InstituteUniversity of PotsdamPotsdamGermany

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