We analyze a model of price competition á la Bertrand in a network environment. Firms only have a limited information on the structure of network: they know the number of potential customers they can attract and the degree distribution of customers. This incomplete information framework stimulates the use of Bayesian-Nash equilibrium. We find that, if there are customers only linked to one firm, but not all of them are, then an equilibrium in randomized strategies fails to exist. Instead, we find a symmetric equilibrium in randomized strategies. Finally, we test our results on US gasoline data. We find empirical evidence consistent with firms playing random strategies.
Bertrand Competition Bayesian- Nash Equilibrium Mobility Index