Dynamic Price Competition with Network Effects

I consider a dynamic model of competition between two proprietary networks. Consumers die with a constant hazard rate and are replaced by new consumers. Firms compete for new consumers to join their network by offering network entry prices (which may be below cost). New consumers have a privately known preference for each network. Upon joining a network, in each period consumers enjoy a benefit which is increasing in network size during that period. Firms receive revenues from new consumers as well as from consumers already belonging to their network. I discuss various properties of the equilibrium, including the pricing function, the system’s expected motion, and the stationary distribution of market shares. I derive several results analytically. I then confirm and extend these results by numerical computation. Finally, I use the model to estimate the barrier to entry create by network effects.