Social media networks have been playing an increasingly more important role for both socialization and information diffusion. Political campaign can gain more supporters by attracting more mass attention and influencing them directly, while commercial campaigns can increase their companies’ profits by expanding social media connection with new users. To build the optimal network structure to influence the whole, this paper studies mathematical models to simulate the users’ behaviours interacting with others in the information provider’s network. The behaviours of concerns include information re-posting and following/unfollowing other users. Linear threshold propagation model is used to determine the re-posting actions, Boundedly Rational User Equilibrium (BRUE) models are used to determine the following or unfollowing actions. Hence, the topology of the network changes and depends on the information provider’s plan to post various kinds of information. A three-level optimization model is proposed to maximize total number of connections, the goal of the top level. The second level simulates user behaviours under BRUE. The third level maximizes the each user’s utility defined in the second level. This paper solves this problem using exact algorithms for a small-scale synthetic network. For a large-scale problem, this paper uses heuristic algorithms based on large neighbourhood search. This paper also discusses possible reasons why the BRUE model may be a more accurate simulation of users’ actions compared to game theory. Comparisons from the BRUE model to game theoretical model show that the BRUE model performs significantly better than game theoretical model.

中文翻译：

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通过社交媒体网络中有限理性的用户行为的多级优化影响网络设计

社交媒体网络在社会化和信息传播中都发挥着越来越重要的作用。政治运动可以通过吸引更多群众注意力并直接影响他们来获得更多支持者，而商业运动可以通过扩大与新用户的社交媒体联系来增加公司的利润。为了建立影响整个网络的最佳网络结构，本文研究了数学模型来模拟用户在信息提供者网络中与他人互动的行为。关注的行为包括信息重新发布以及关注/取消关注其他用户。线性阈值传播模型用于确定重新发布操作，有界理性用户平衡（BRUE）模型用于确定以下或后续操作。因此，网络的拓扑结构会发生变化，并取决于信息提供者发布各种信息的计划。提出了一个三级优化模型，以最大程度地提高连接总数，这是顶层的目标。第二级模拟BRUE下的用户行为。第三级最大化第二级中定义的每个用户的实用程序。本文针对小型合成网络使用精确算法解决了此问题。对于大规模问题，本文使用基于大邻域搜索的启发式算法。本文还讨论了与游戏理论相比，BRUE模型可能更准确地模拟用户行为的可能原因。从BR​​UE模型到博弈论模型的比较表明，BRUE模型的性能明显好于博弈论模型。