Duopoly Competition with Network Effects in Discrete Choice Models.

It has been realized for a long time that network effects play an important role in how market participants compete with each other. Arguably, companies like Facebook and Google are able to gain immense market power by leveraging the network effects of their consumers, despite potential competitors. This paper investigates how the dynamics play out in duopoly competition. We find that when the network effects per unit of consumption are weak, the competitors can co-exist and gain even market shares. As network effects become stronger, it is unstable, and even impossible, for the firms to coexist, and one firm emerges victorious, taking the majority of the market. The study provides a theoretical analysis for commonly observed market phenomena. It may also have implications for antitrust legislation: Special policies need to be created to maintain a competitive market structure for products and services with strong network effects. 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. [ABSTRACT FROM AUTHOR]