Bertrand competition in networks

Abstract

We study price-of-anarchy type questions in two-sided markets with combinatorial consumers and limited supply sellers. Sellers own edges in a network and sell bandwidth at fixed prices subject to capacity constraints; consumers buy bandwidth between their sources and sinks so as to maximize their value from sending traffic minus the prices they pay to edges. We characterize the price of anarchy and price of stability in these "network pricing" games with respect to two objectives-the social value (social welfare) of the consumers, and the total profit obtained by all the sellers. In single-source single-sink networks we give tight bounds on these quantities based on the degree of competition, specifically the number of monopolistic edges, in the network. In multiple-source single-sink networks, we show that equilibria perform well only under additional assumptions on the network and demand structure. © 2008 Springer-Verlag Berlin Heidelberg.