Optimal pricing in social networks under fuzzy environment

In this paper, we study optimal pricing strategy decisions of the monopolist in a social network under a fuzzy environment, in which consumers experience a nonnegative network effect that is influenced by their neighbors’ consumption level, the extent to which they are affected is considered as a fuzzy variable. To derive the equilibrium solution, we establish a two-stage game model for decision processes in consumer social networks. Utilizing the backward induction, we first get the expected consumption equilibrium, then figure out the matrix expression of unique pricing equilibrium by maximizing the monopolist’s profit. In addition, we introduce Fuzzy Bonacich Centrality, and find out components of the price each consumer charged by the monopolist in a fuzzy network, this points out the importance of the monopolist knowing consumer network structure. By conducting numerical studies, we find that the network effect plays an essential role in deciding pricing strategies in fuzzy social networks, but fuzziness would weaken this impact. For social networks with fuzziness existing, the monopolist should choose discriminatory pricing strategy to benefit most. The results of our model can provide valuable managerial insights when helping the monopolist make pricing decisions.