arXiv 1909.097992019-09-21cs.GT

论高价链接的无政府代价

On the Price of Anarchy for High-Price Links

Carme Àlvarez, Arnau Messegué

备注：: 14 pages, 4 figures

摘要：

研究了Fabrikant，Luthra，Maneva，Papadimitriou和Shenker在2003年提出的经典网络创造博弈模型中的纳什均衡和无政府状态的无政府代价。这是一个自私的网络创建模型，其中玩家对应于网络中的节点，并且他们中的每一个都可以以预定价格$α> 0$创建到其他$n-1$玩家的链接。玩家的目标是最小化她购买边的成本和她使用结果网络的成本之和。该模型的一个主要论点是，无政府状态的无政府代价，即缺乏协调的相对成本，对所有PDMATHAMO来说都是恒定的。这一猜想已被证实为$α= O(n^{1-δ})$与$δ\geq 1/\log n$和$α> 4n-13$。最著名的无政府无政府代价上限是$2^{O(\sqrt{\log n})}$。我们给出了新的见解$α> n$的纳什均衡的结构，我们扩大了参数$α$的范围，无政府状态的无政府代价是恒定的。具体来说，我们证明，对于任何小$ε>0$，无政府状态无政府代价是恒定的$α> n(1+ε)$，任何非平凡的纳什均衡的任何biconconnected组件，如果存在的话，最多有一个恒定数目的节点。

英文摘要：

We study Nash equilibria and the price of anarchy in the classic model of Network Creation Games introduced by Fabrikant, Luthra, Maneva, Papadimitriou and Shenker in 2003. This is a selfish network creation model where players correspond to nodes in a network and each of them can create links to the other $n-1$ players at a prefixed price $α> 0$. The player's goal is to minimise the sum of her cost buying edges and her cost for using the resulting network. One of the main conjectures for this model states that the price of anarchy, i.e. the relative cost of the lack of coordination, is constant for all $α$. This conjecture has been confirmed for $α= O(n^{1-δ})$ with $δ\geq 1/\log n$ and for $α> 4n-13$. The best known upper bound on the price of anarchy for the remaining range is $2^{O(\sqrt{\log n})}$. We give new insights into the structure of the Nash equilibria for $α> n$ and we enlarge the range of the parameter $α$ for which the price of anarchy is constant. Specifically, we prove that for any small $ε>0$, the price of anarchy is constant for $α> n(1+ε)$ by showing that any biconnected component of any non-trivial Nash equilibrium, if it exists, has at most a constant number of nodes.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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