论文标题
病毒营销的时空预算分配政策设计
Space-time budget allocation policy design for viral marketing
论文作者
论文摘要
当社交网络(例如消费者)的代理人不仅受邻居的影响,而且还受到称为营销人员的外部影响力实体的影响时,我们正式解决了意见动态问题。有影响力的实体试图通过使用特定的影响力预算,尽可能地将整体意见与所需意见保持联系。我们假设该实体的外在影响发生在离散时间广告活动中;因此,总体闭环的意见动力学变成了线性冲动(混合)。解决的主要技术问题是找出营销人员应如何在时间(通过营销活动中)和太空(在代理商中)分配其预算,以使代理商的意见尽可能接近所需的意见。我们的主要结果表明,营销人员必须根据其初始状况,社交图中的影响力和集群的大小来优先考虑某些代理人。相应的时空分配问题是针对几种实用感兴趣的特殊案例制定和解决的。有价值的见解可以从我们的分析中提取。例如,在大多数情况下,我们证明营销人员有兴趣在流程开始时投资大部分预算,并且根据著名的填充水分配规则应在代理商中共享预算。数值示例说明了分析。
We address formally the problem of opinion dynamics when the agents of a social network (e.g., consumers) are not only influenced by their neighbors but also by an external influential entity referred to as a marketer. The influential entity tries to sway the overall opinion as close as possible to a desired opinion by using a specific influence budget. We assume that the exogenous influences of the entity happen during discrete-time advertising campaigns; consequently, the overall closed-loop opinion dynamics becomes a linear-impulsive (hybrid) one. The main technical issue addressed is finding how the marketer should allocate its budget over time (through marketing campaigns) and over space (among the agents) such that the agents' opinion be as close as possible to the desired opinion. Our main results show that the marketer has to prioritize certain agents over others based on their initial condition, their influence power in the social graph and the size of the cluster they belong to. The corresponding space-time allocation problem is formulated and solved for several special cases of practical interest. Valuable insights can be extracted from our analysis. For instance, for most cases, we prove that the marketer has an interest in investing most of its budget at the beginning of the process and that budget should be shared among agents according to the famous water-filling allocation rule. Numerical examples illustrate the analysis.