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首页> 外文期刊>ACM Transactions on Internet Technology >A Game Theoretic Model for the Formation of Navigable Small-World Networks-The Tradeoff between Distance and Reciprocity
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A Game Theoretic Model for the Formation of Navigable Small-World Networks-The Tradeoff between Distance and Reciprocity

机译：可通航小世界网络形成的游戏理论模型 - 距离与互惠之间的权衡

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Kleinberg proposed a family of small-world networks to explain the navigability of large-scale real-world social networks. However, the underlying mechanism that drives real networks to be navigable is not yet well understood. In this article, we present a game theoretic model for the formation of navigable small-world networks. We model the network formation as a game called the Distance-Reciprocity Balanced (DRB) game in which people seek for both high reciprocity and long-distance relationships. We show that the game has only two Nash equilibria: One is the navigable small-world network, and the other is the random network in which each node connects with each other node with equal probability, and any other network state can reach the navigable small world via a sequence of best-response moves of nodes. We further show that the navigable small-world equilibrium is very stable-(a) no collusion of any size would benefit from deviating from it; and (b) after an arbitrary deviations of a large random set of nodes, the network would return to the navigable small world as soon as every node takes one best-response step. In contrast, for the random network, a small group collusion or random perturbations is guaranteed to bring the network out of the random-network equilibrium and move to the navigable network as soon as every node takes one best-response step. Moreover, we show that navigable small-world equilibrium has much better social welfare than the random network, and we provide the price-of-anarchy and price-of-stability results of the game. Our empirical evaluation further demonstrates that the system always converges to the navigable network even when limited or no information about other players' strategies is available, and the DRB game simulated on real-world networks leads to navigability characteristic that is very close to that of the real networks, even though the real-world networks have non-uniform population distributions different from Kleinberg's small-world model. Our theoretical and empirical analyses provide important new insight on the connection between distance, reciprocity, and navigability in social networks.
机译：Kleinberg提出了一家小世界网络，以解释大型现实世界社交网络的导航性。然而，驱动真实网络即可导航的潜在机制尚不清楚。在本文中，我们为导航小世界网络的形成提供了一种游戏理论模型。我们将网络形成建模为一个名为距离互惠平衡（DRB）游戏的游戏，其中人们寻求高互惠和长距离关系。我们表明游戏只有两个纳什均衡：一个是可通航的小世界网络，另一个是每个节点以相同的概率与彼此连接的随机网络，并且任何其他网络状态都可以达到可导航的小型通过一系列最佳响应的节点动作。我们进一步表明，可通航的小世界平衡非常稳定 - （a）没有任何尺寸的勾结将受益于偏离它; （b）在大型随机节点的任意偏差之后，只要每个节点都采取一个最佳响应步骤，网络将返回到可通航的小世界。相反，对于随机网络，保证小组勾集或随机扰动，以便在每个节点采用一个最佳响应步骤时立即将网络从随机网络平衡中带出并移动到可通航网络。此外，我们表明，通航的小世界均衡与随机网络的社会福利有多好，我们提供了比赛的性能和稳定性的稳定性结果。我们的经验评估进一步表明，即使有限或没有关于其他玩家的策略的信息，系统始终将其始终收敛到可通航网络，并且在真实网络上模拟的DRB游戏导致导航性是非常接近的导航性特性实际网络，即使真实世界网络具有不同于Kleinberg的小世界模型的非统一人口分布。我们的理论和实证分析为社交网络中的距离，互惠和导航性之间的连接提供了重要的新洞察。

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