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.

中文翻译：

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关于网络创造游戏的树猜想

自私的网络创作专注于从游戏理论的角度对现实世界的网络进行建模。Fabrikant等人的经典模型之一。（2003年）是网络创建游戏，其中代理对应于网络中的节点，这些节点以每条边的α的价格购买入射边，以最大程度地减少其与所有其他节点的总距离。该模型已经过充分研究，但仍然存在有趣的开放问题。最著名的猜想状态无政府状态的价格是所有常数α并且对于α ≥ ň所有平衡网络是树。我们介绍了一种用于分析稳定网络的高边价α的新技术并用它来改善后一种猜想的最著名界限。特别地，我们表明，对于α > 4 n -13，所有均衡网络都必须是树，这意味着在此α范围内无政府状态价格不变。此外，我们还提高了平衡树无政府状态价格的恒定上限。