  With the advent of social media, different companies often promote competing
products simultaneously for word-of-mouth diffusion and adoption by users in
social networks. For such scenarios of competitive diffusion, prior studies
show that the weaker product will soon become extinct (i.e., "winner takes
all"). It is intriguing to observe that in practice, however, competing
products, such as iPhone and Android phone, often coexist in the market. This
discrepancy may result from many factors such as the phenomenon that a user in
the real world may not spread its use of a product due to dissatisfaction of
the product or privacy protection. In this paper, we incorporate users' privacy
for spreading behavior into competitive diffusion of two products and develop a
problem formulation for privacy-aware competitive diffusion. Then, we prove
that privacy-preserving mechanisms can enable a "coexistence equilibrium"
(i.e., two competing products coexist in the equilibrium) in competitive
diffusion over social networks. In addition to the rigorous analysis, we also
demonstrate our results with experiments over real network topologies.
