Cost effective campaigning in social networks

Campaigners are increasingly using online social networking platforms for promoting products, ideas and information. A popular method of promoting a product or even an idea is incentivizing individuals to evangelize the idea vigorously by providing them with referral rewards in the form of discounts, cash backs, or social recognition. Due to budget constraints on scarce resources such as money and manpower, it may not be possible to provide incentives for the entire population, and hence incentives need to be allocated judiciously to appropriate individuals for ensuring the highest possible outreach size. We aim to do the same by formulating and solving an optimization problem using percolation theory. In particular, we compute the set of individuals that are provided incentives for minimizing the expected cost while ensuring a given outreach size. We also solve the problem of computing the set of individuals to be incentivized for maximizing the outreach size for given cost budget. The optimization problem turns out to be non trivial; it involves quantities that need to be computed by numerically solving a fixed point equation. Our primary contribution is, that for a fairly general cost structure, we show that the optimization problems can be solved by solving a simple linear program. We believe that our approach of using percolation theory to formulate an optimization problem is the first of its kind. (C) 2016 Elsevier B.V. All rights reserved.