22 / 2007 Congestion pricing , Bertrand oligopoly , and forward contracts for bandwidth

We develop a pricing game modelling a monopoly and an oligopoly of Internet Service Providers selling bandwidth on two complementary segments of a multi-provider communication network. We consider pricing behavior when the oligopolists have previously sold part of their capacity by means of forward contracts, assuming all prices are set simultaneously. We find the equilibria in pure strategies where they exist. Where they do not exist, we find an equilibrium allowing the oligopolists to use mixed strategies. This requires solving an extension of the Bertrand-Edgeworth game with symmetric capacities and asymmetric contracting levels. Although providers have an incentive to sell forward contracts to insure against demand uncertainty, contracting also commits them to lower prices in general. We find that any equilibrium with contracting levels is asymmetric with a unique provider choosing the lowest level of contracting. By refraining from signing too many contracts, this provider guarantees a high general downstream price level at a private cost. An increase in the lowest contracting level results in negative marginal externalities on all other oligopolists. On the other hand, an increase in any other contracting level causes positive marginal externalities.