A k-hop Collaborate Game Model: Adaptive Strategy to Maximize Total Revenue

In Online Social Networks (OSNs), interpersonal communication and information sharing are happening all the time, and it is real-time. When a user initiates an activity in OSNs, immediately, he/she will have a certain influence in his/her friendship circle naturally, some users in the initiator's friendship circle will be attracted to participate in this activity. Based on such a fact, we design a k-hop Collaborate Game Model, which means that an activity initiated by a user can only influence those users whose distance are within k-hop from this initiator in OSNs. Besides, we introduce the problem of Revenue Maximization under k-hop Collaborate Game (RMKCG), which identifies a limited number of initiators in order to obtain revenue as much as possible. Collaborate Game Model describes in detail how to quantify revenue and the logic behind it. We do not know how many followers would be generated from an activity in advance, thus, we need to adopt an adaptive strategy, where the decision who is the next potential initiator depends on the results of past decisions. Adaptive RMKCG problem can be considered as a new stochastic optimization problem, and we prove it is NP-hard, adaptive monotone, but not adaptive submodular. But in some special cases, it is adaptive submodular and an adaptive greedy strategy can obtain a $(1-1/e)$-approximation by adaptive submodularity theory. Due to the complexity of our model, it is hard to compute the marginal gain for each candidate user, then, we propose a convenient and efficient computational method. The effectiveness and correctness of our algorithms are validated by heavy simulation on real-world social networks eventually.