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On Studying the Impact of Uncertainty on Behavior Diffusion in Social Networks

Unlike traditional epidemic virus spreading, behavior diffusion in social networks is conducted by rational users, who would make strategic choices instead of being randomly infected with some probability. Specifically, individuals always try to maximize their utilities through rationally selecting specific behaviors (adopting a new product, or spreading a rumor, etc.). However, utility obtained by an individual, naturally contains uncertainty, and it may stem from two sources: users' imperfect and incomplete knowledge about others, and the inherently stochastic property in human behavior. Thus, it is imperative to model and analyze the diffusion pattern under the resulting uncertainty in social networks, which, however, has not yet been deeply examined by the existing works. This paper deeply explores the pattern of gossip diffusion in social networks when uncertainty exists in users' decision making. In detail, the innovative results provided in this paper are: first, inspired by random utility theory, we formulate the diffusion model based on mixed logit model that allows for user's uncertainty in determining whether to adopt a specific strategy; second, the formal analysis framework characterizing the diffusion process is derived through the approximation method of mean field theory; finally, we explore the extensive applicability of our proposed analysis framework through modeling rumor diffusion in social networks as a coordination game. Our findings are, for various structural characteristics, small uncertainty can significantly speed up the diffusion of gossip; furthermore, social networks with scale-free property can facilitate the gossip diffusion in the easiest way, but, the range of uncertainty factor that can maximize gossip diffusion is the smallest. The obtained results perfectly comply with the philosophical saying about rumor diffusion in real social life: easy come, easy go.