Geometric Network Creation Games

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 277-315, March 2024.
Abstract. Network creation games are a well-known approach for explaining and analyzing the structure, quality, and dynamics of real-world networks that evolved via the interaction of selfish agents without a central authority. In these games selfish agents corresponding to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games 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 depend 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. [Proceedings of PODC ’03, ACM, 2003, pp. 347–351] 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 nonconstant bound on the price of anarchy for the metric version and a slightly weaker upper bound for the nonmetric 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 the classical network design problem. Thus, low-cost equilibria of our game correspond to decentralized and stable approximations of the optimum network design.