Optimal selling scheme in social networks: hierarchical signaling, sequential selling, and chain structure

We study the optimal selling scheme when a seller sells a product/service with a positive consumption externality, and customers are uncertain about the product's/service's value. Because early adopters learn this value, we consider the customers' intrinsic signaling incentives and positive feedback effects. Allowing the seller to choose the sequence of customers' decisions (as an endogenous hierarchy) implies that signaling takes place in multiple rounds. To tackle this hierarchical signaling problem, we develop a novel dynamic‐programming approach that yields analytical expressions of the equilibrium outcomes. The profit‐maximizing structure turns out to be a chain in which the seller sells to the customers one by one. The sequential selling scheme is not only profitable for the seller but also beneficial to the society. The profit‐maximizing pricing exhibits a cream‐skimming property–decreasing prices along the sequence. The lack of seller's commitment is detrimental to the social welfare; nonetheless, the sequential selling still boosts up the seller's profit. When customers are allowed to freely disclose their quantity decisions to others, they willingly comply with the seller's plan of information transmissions. Despite the inherent value uncertainty, the optimal usage of information transmissions requires deliberate restricted access to information among customers. Our result also suggests some congruence between the profit and welfare maximization.