  When a new product enters a market already dominated by an existing product,
will it survive along with this dominant product? Most of the existing works
have shown the coexistence of two competing products spreading/being adopted on
overlaid graphs with same set of users. However, when it comes to the survival
of a weaker product on the same graph, it has been established that the
stronger one dominates the market and wipes out the other. This paper makes a
step towards narrowing this gap so that a new/weaker product can also survive
along with its competitor with a positive market share. Specifically, we
identify a locally optimal set of users to induce a community that is targeted
with advertisement by the product launching company under a given budget
constraint. To this end, we model the system as competing
Susceptible-Infected-Susceptible (SIS) epidemics and employ perturbation
techniques to quantify and attain a positive market share in a cost-efficient
manner. Our extensive simulation results with real-world graph dataset show
that with our choice of target users, a new product can establish itself with
positive market share, which otherwise would be dominated and eventually wiped
out of the competitive market under the same budget constraint.
