Dynamic expansions of social followings with lotteries and give-aways

The problem of how to attract a robust following on social media is one of the most pressing for influencers. We study a common practice on popular microblogging platforms such as Twitter, of influencers' expanding their followings by running lotteries and giveaways. We are interested in how the lottery size and the seeding decisions influence the information propagation and the final reward for such a campaign. We construct an information-diffusion model based on a random graph, and show that the market demand curve of the lottery reward via the promotion of the social network is "S"-shaped. This property lays a foundation for finding the optimal lottery size. Second, we observe that (i) dynamic seeding could re-stimulate the spread of information and (ii) with a fixed budget, seeding at two fixed occasions is always better than seeding once at the beginning. This observation motivates us to study the joint optimization of lottery size and adaptive seeding. We model the adaptive seeding problem as a Markov Decision Process. We find the monotonicity of the value functions and trends in the optimal actions, and we show that with adaptive seeding, the reward curve is approximately "S"-shaped with respect to the lottery size.