@misc{BiloFriedrichLenzneretal.2019,
  author    = {Bilo, Davide and Friedrich, Tobias and Lenzner, Pascal and Melnichenko, Anna},
  title     = {Geometric Network Creation Games},
  series = {SPAA '19: The 31st ACM Symposium on Parallelism in Algorithms and Architectures},
  journal   = {SPAA '19: The 31st ACM Symposium on Parallelism in Algorithms and Architectures},
  publisher = {Association for Computing Machinery},
  address   = {New York},
  isbn      = {978-1-4503-6184-2},
  doi       = {10.1145/3323165.3323199},
  pages     = {323 -- 332},
  year      = {2019},
  abstract  = {Network Creation Games are a well-known approach for explaining and analyzing the structure, quality and dynamics of real-world networks like the Internet and other infrastructure networks which evolved via the interaction of selfish agents without a central authority. In these games selfish agents which correspond to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games has only considered the creation of networks with unit-weight edges. In practice, e.g. when constructing a fiber-optic network, the choice of which nodes to connect and also the induced price for a link crucially depends on the distance between the involved nodes and such settings can be modeled via edge-weighted graphs. We incorporate arbitrary edge weights by generalizing the well-known model by Fabrikant et al. [PODC'03] to edge-weighted host graphs and focus on the geometric setting where the weights are induced by the distances in some metric space. In stark contrast to the state-of-the-art for the unit-weight version, where the Price of Anarchy is conjectured to be constant and where resolving this is a major open problem, we prove a tight non-constant bound on the Price of Anarchy for the metric version and a slightly weaker upper bound for the non-metric case. Moreover, we analyze the existence of equilibria, the computational hardness and the game dynamics for several natural metrics. The model we propose can be seen as the game-theoretic analogue of a variant of the classical Network Design Problem. Thus, low-cost equilibria of our game correspond to decentralized and stable approximations of the optimum network design.},
  language  = {en}
}