Duopoly Competition with Network Effects in Discrete Choice Models

We consider two firms selling products to a market of network-connected customers. Each firm is selling one product, and the two products are substitutable. The customers make purchases based on the multinomial logit model, and the firms compete for their purchasing probabilities. We characterize possible Nash equilibria for homogeneous network interactions and identical firms: When the network effects are weak, there is a symmetric equilibrium that the two firms evenly split the market; when the network effects are strong, there exist two asymmetric equilibria additionally, in which one firm dominates the market; interestingly, when the product quality is low and the network effects are neither too weak nor too strong, the resulting market equilibrium is never symmetric, although the firms are ex ante symmetric. We extend these results along multiple directions. First, when the products have heterogeneous qualities, the firm selling inferior product can still retain market dominance in equilibrium due to the strong network effects. Second, when the network effects are heterogeneous, customers with higher social influences or larger price sensitivities are more likely to purchase either product in the symmetric equilibrium. Third, when the network consists of two communities, market segmentation may arise. Fourth, we extend to the dynamic game when the network effects build up over time to explain the first-mover advantage.