论文标题
在网络中心性最大化游戏上
On a Network Centrality Maximization Game
论文作者
论文摘要
我们研究了一个网络编队游戏，其中$ n $玩家被标识为要形成的有向图的节点，选择在哪里连接其即将发出的链接，以最大程度地提高其Pagerank Centrarity。具体而言，每个玩家$ i $的动作都由预定的数字$ d_i $ d_i $ d_i $ d_i $ d_i $，而她的实用程序是她自己的pagerank中心性，这是由于所有玩家的动作而导致的。我们表明这是一个潜在的游戏，最好的响应信函总是表现出本地结构，因为对于节点$ i $，链接到其他距离的节点从来都不是方便的，而这些节点的传入距离超过了$ d_i $。然后，我们研究了该游戏的平衡，确定图形是（严格，经常性）NASH平衡的必要条件。此外，在同质的情况下，玩家都具有相同的数字$ d $ of-links，我们表征了潜在的最大化平衡的结构，在特殊情况下，$ d = 1 $ and $ d = 2 $，我们提供了一组（严格的，重复的）nash equilibria的完整分类。我们的分析特别表明，所考虑的形成机制导致了未指向和断开或松散连接的网络的出现。
We study a network formation game where $n$ players, identified with the nodes of a directed graph to be formed, choose where to wire their outgoing links in order to maximize their PageRank centrality. Specifically, the action of every player $i$ consists in the wiring of a predetermined number $d_i$ of directed out-links, and her utility is her own PageRank centrality in the network resulting from the actions of all players. We show that this is a potential game and that the best response correspondence always exhibits a local structure in that it is never convenient for a node $i$ to link to other nodes that are at incoming distance more than $d_i $ from her. We then study the equilibria of this game determining necessary conditions for a graph to be a (strict, recurrent) Nash equilibrium. Moreover, in the homogeneous case, where players all have the same number $d$ of out-links, we characterize the structure of the potential maximizing equilibria and, in the special cases $ d=1 $ and $ d=2 $, we provide a complete classification of the set of (strict, recurrent) Nash equilibria. Our analysis shows in particular that the considered formation mechanism leads to the emergence of undirected and disconnected or loosely connected networks.
