  We consider the problem of devising incentive strategies for viral marketing
of a product. In particular, we assume that the seller can influence
penetration of the product by offering two incentive programs: a) direct
incentives to potential buyers (influence) and b) referral rewards for
customers who influence potential buyers to make the purchase (exploit
connections). The problem is to determine the optimal timing of these programs
over a finite time horizon. In contrast to algorithmic perspective popular in
the literature, we take a mean-field approach and formulate the problem as a
continuous-time deterministic optimal control problem. We show that the optimal
strategy for the seller has a simple structure and can take both forms, namely,
influence-and-exploit and exploit-and-influence. We also show that in some
cases it may optimal for the seller to deploy incentive programs mostly for low
degree nodes. We support our theoretical results through numerical studies and
provide practical insights by analyzing various scenarios.
