@article{BiloLenzner2019,
  author    = {Bil{\`o}, Davide and Lenzner, Pascal},
  title     = {On the tree conjecture for the network creation game},
  series = {Theory of computing systems},
  volume    = {64},
  journal   = {Theory of computing systems},
  number    = {3},
  publisher = {Springer},
  address   = {New York},
  issn      = {1432-4350},
  doi       = {10.1007/s00224-019-09945-9},
  pages     = {422 -- 443},
  year      = {2019},
  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 alpha 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 alpha and that for alpha >= n all equilibrium networks are trees. We introduce a novel technique for analyzing stable networks for high edge-price alpha and employ it to improve on the best known bound for the latter conjecture. In particular we show that for alpha > 4n - 13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of alpha. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.},
  language  = {en}
}