We consider the following network pricing game: sellers own bandwidth on edges in the network; consumers are source-sink pairs and are interested in buying bandwidth along paths between their end-points; each seller prices bandwidth on her own edge so as to maximize her profit subject to demand and supply constraints; each user picks the path(s) that bring her the most utility. Our goal is to study the performance of equilibria arising in this game as a function of the degree of competition in the game, the network topology, and the demand structure. Economists have traditionally studied such questions in single-item two-sided markets. It is well known, for example, that monopolies cause inefficiency in a market by charging high prices, whereas competition has the effect of driving prices down and operating efficiently. Our work extends the classical Bertrand model of competition from economics to the network setting. We show that equilibria in this game depend closely on the (sparsest) cut structure of the network; moreover, competition is not sufficient for guaranteeing efficient operation of the network, and additional requirements on the demand distribution are required.