In this paper, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows a hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed recently in [1], we prove that although the marketers are in competition and therefore create tension in the network, the network reaches a consensus. Exploiting this key result, we propose a coopetition marketing strategy which combines the one-shot Nash equilibrium actions and a policy of no advertising. Under reasonable sufficient conditions, it is proved that the proposed coopetition strategy profile Pareto-dominates the one-shot Nash equilibrium strategy. This is a very encouraging result to tackle the much more challenging problem of designing Pareto-optimal and equilibrium strategies for the considered dynamical marketing game.

中文翻译：

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通过社交网络分配营销资源：长期分析

在本文中，我们考虑受邻居和外部影响实体（营销人员）共同影响的消费者网络。消费者的意见遵循混合动力，其意见跳跃是由于营销活动。通过使用最近在 [1] 中提出的相关静态博弈模型，我们证明尽管营销人员处于竞争状态并因此在网络中制造紧张局势，但网络达成了共识。利用这一关键结果，我们提出了一种竞争营销策略，该策略结合了一次性纳什均衡动作和无广告策略。在合理的充分条件下，证明了所提出的竞争策略配置文件帕累托主导了一次性纳什均衡策略。