Dynamic pricing strategies for social networks in the presence of externalities

We propose a dynamic pricing strategy for maximizing the revenue of a seller who wishes to sell a divisible service (good) to buyers (agents) embedded in a social network. We investigate the case where the seller can perfectly price discriminate the socially interconnected buyers with positive social influences on each other. We assume that each buyer purchases a non-negative quantity of the service depending both on her internal valuations and on the purchases of her neighbors in the social network. We relax the usual game theoretic assumption of strategic agents and assume a more realistic model of myopic buyers who choose actions that maximize their present utility and do not take into account the effect of their current actions to their future payoffs. We explore the space of dynamic pricing strategies where the seller approaches the buyers sequentially and repeatedly in multiple rounds of a selected order. We propose a dynamic policy for networks with reciprocating agents and compare its performance against an existing static policy that achieves the equilibrium consumption of the buyers. We show that our sequential dynamic pricing policy yields a greater revenue value for the seller and also drives the aggregate social welfare to a higher level than what is achievable by even the best equilibrium. Further, the computational complexity of each new round is cubic in the size of the social network. Our results indicate that dynamics provide a means to improve both seller and buyer objectives even though the strategy is designed specifically to maximize the seller´s revenue.