Bertrand Competition in Networks
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.
KeywordsNash Equilibrium Capacity Constraint Demand Curve Pure Nash Equilibrium Bertrand Competition
Unable to display preview. Download preview PDF.
- 3.Anshelevich, E., Shepherd, B., Wilfong, G.: Strategic network formation through peering and service agreements. In: Foundations of Computer Science (2006)Google Scholar
- 4.Chawla, S., Roughgarden, T.: Bertrand competition in networks, http://www.cs.wisc.edu/shuchi/papers/Bertrand-competition.pdf
- 5.Cole, R., Dodis, Y., Roughgarden, T.: Pricing network edges for heterogeneous selfish users. In: Proc. 34th ACM Symp. Theory of Computing (2003)Google Scholar
- 6.Estan, C., Akella, A., Banerjee, S.: Achieving good end-to-end service using bill-pay. In: HOTNETS-V (2006)Google Scholar
- 7.Fleischer, L., Jain, K., Mahdian, M.: Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games. In: Proc. 45th IEEE Symp. Foundations of Computer Science, pp. 277–285 (2004)Google Scholar
- 9.Hayrapetyan, A., Tardos, É., Wexler, T.: A network pricing game for selfish traffic. In: Proc. Symp. Principles of distributed Computing, pp. 284–291 (2005)Google Scholar
- 11.Mas-Colell, Whinston, Green: Microeconomic Theory. Oxford (1995)Google Scholar
- 12.Odlyzko, A.: Paris metro pricing for the internet. In: Proc. 1st ACM Conf. Electronic Commerce, pp. 140–147 (1999)Google Scholar
- 13.Ozdaglar, A., Srikant, R.: Incentives and pricing in communication networks. In: Algorithmic Game Theory, Cambridge Press, Cambridge (2007)Google Scholar
- 17.Weintraub, G.Y., Johari, R., Van Roy, B.: Investment and market structure in industries with congestion. (Unpublished manuscript, 2007) Google Scholar