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 α ≥ n 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.
Highlights
Many important networks, e.g. the Internet or social networks, have been created in a decentralized way by selfishly acting agents
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
A thorough understanding of the structural properties of such equilibrium networks is the key. We contribute to this endeavor by providing new insights into the structure of equilibrium networks for one of the classical models of selfish network creation [24]
Summary
E.g. the Internet or social networks, have been created in a decentralized way by selfishly acting agents Modeling and understanding such networks is an important challenge for researchers in the fields of Computer Science, Network Science, Economics and Social Sciences. A thorough understanding of the structural properties of such equilibrium networks is the key We contribute to this endeavor by providing new insights into the structure of equilibrium networks for one of the classical models of selfish network creation [24]. In this model, agents correspond to nodes in a network and can buy costly links to other nodes to minimize their total distance in the created network. Our insights yield improved bounds on the price of anarchy and significant progress towards settling the so-called tree conjecture [24, 36]
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