Duopoly Competition with Network Effects in Discrete Choice Models

Abstract

We consider two firms that sell substitutable products to a market of network-connected customers. 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 three directions. First, when the products have heterogeneous qualities, we establish that the firm selling inferior product can still retain market dominance due to the strong network effects. Nevertheless, when the quality difference is sufficiently large, the quality superior firm can secure its dominating position. 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, we show that market segmentation can arise: one product is dominating in one community, while the other product is popular in the other community.

Keywords: duopoly competition, network effects, multinomial logit model, Cournot competition