While the influence maximization problem (IMP) which studies how to trigger a large cascade in Online Social Networks (OSNs) by properly selecting seed nodes has been extensively studied in the past decade, one important and practical issue on how these seed nodes or celebrities will get paid for promoting cascades is seldom addressed. In order to get selected by the advertising platform and to maximize his/her own utility, it is natural for each celebrity to determine his/her price of promoting cascades based on other celebrities' decisions and his/her power of influence. In this paper, we formulate the problem of determining prices by celebrities as a pricing game, with celebrities as players. We show that celebrity selection by the advertising platform is NP-hard, and assume that the advertising platform will adopt the simple greedy algorithm that is widely used in IMP. Under this assumption, we study the pure Nash equilibrium of the pricing game among celebrities. In particular, we prove that while equilibrium exists and is unique when there are only two or three players, the equilibrium is not guaranteed to exist in cases of four or more players.
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