We study competitive influence propagation in social networks based on Independent Cascade (IC) model. First we propose two new models, in both of which each individual in the network is allowed to propagate multiple influences to its neighbors. In the first Deadline Independent Cascade (DIC) model, each individual has a deadline of following the final single influence and before that it may accept different influences. In the second Latency Independent Cascade (LIC) model, once an individual firstly receives any influence, it has a latency to make the final decision and in the latency it continues receiving influences. Second we analyze the combinatorial properties of our proposed models. We prove that the influence spread under DIC model is monotone and sub modular, which implies that the last influence source has a strategy that returns at least 1 - 1/e of the best response. We also give examples showing that the influence spread under LIC model is neither monotone nor sub modular, which implies that even for the last influence source, it is hard to find the strategy with guaranteed performance.
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