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arXiv 1202.2209cs.SIcs.GTphysics.soc-ph
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在社交网络中选择产品

Choosing Products in Social Networks

Sunil Simon, Krzysztof R. Apt

摘要:

我们研究了形成社会网络的代理商采用产品的后果。为此,我们使用Apt和Markakis,arXiv:1105.2434中介绍的阈值模型,其中受其邻居影响的节点可以采用几种替代方案中的一种,并将每个社交网络与代理之间的策略博弈相关联。不选择任何产品的可能性导致两种特殊类型的(纯)纳什均衡。我们表明,这样的游戏可能没有纳什均衡,并确定存在的纳什均衡,也是一种特殊类型,是NP-完全的。当社交网络的底层图是DAG、简单循环或没有源节点时,情况会发生变化。对于这三类,我们确定建立(特殊类型的)纳什均衡是否存在的复杂性。我们还澄清了这些类别的游戏的状态和有限改进属性(FIP)的复杂性。此外,我们引入了一个新的属性的一致FIP,这是满足时,底层图是一个简单的循环,但确定它是co-NP-hard在一般情况下,也当底层图没有源节点。后者的复杂性结果也适用于验证的性质是一个弱非循环的游戏。

英文摘要:

We study the consequences of adopting products by agents who form a social network. To this end we use the threshold model introduced in Apt and Markakis, arXiv:1105.2434, in which the nodes influenced by their neighbours can adopt one out of several alternatives, and associate with such each social network a strategic game between the agents. The possibility of not choosing any product results in two special types of (pure) Nash equilibria. We show that such games may have no Nash equilibrium and that determining the existence of a Nash equilibrium, also of a special type, is NP-complete. The situation changes when the underlying graph of the social network is a DAG, a simple cycle, or has no source nodes. For these three classes we determine the complexity of establishing whether a (special type of) Nash equilibrium exists. We also clarify for these categories of games the status and the complexity of the finite improvement property (FIP). Further, we introduce a new property of the uniform FIP which is satisfied when the underlying graph is a simple cycle, but determining it is co-NP-hard in the general case and also when the underlying graph has no source nodes. The latter complexity results also hold for verifying the property of being a weakly acyclic game.

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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