Oligopoly pricing in congested networks

In this paper we study the problem of oligopoly pricing in congested markets when the demand faced by every firm is stochastic. In particular, we consider a general network, where every link is owned by a firm which charges prices in order to maximize its profits. In this environment we show the existence of a pure strategy price equilibrium, where the latency functions are assumed to satisfy continuity, monotonicity and convexity. Given this existence result, we show how to compute bounds for the inefficiency and how the result can be adapted to study price and capacity competition.