Journal of the ACM (JACM)
A BGP-based mechanism for lowest-cost routing
Distributed Computing - Special issue: PODC 02
ACM Transactions on Algorithms (TALG)
Trading networks with price-setting agents
Proceedings of the 8th ACM conference on Electronic commerce
Bertrand Competition in Networks
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Network Formation and Routing by Strategic Agents Using Local Contracts
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
The price of anarchy in bertrand games
Proceedings of the 10th ACM conference on Electronic commerce
Pricing, competition, and routing in relay networks
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Putting BGP on the right path: a case for next-hop routing
Hotnets-IX Proceedings of the 9th ACM SIGCOMM Workshop on Hot Topics in Networks
An analytical approach to the study of cooperation in wireless ad hoc networks
IEEE Transactions on Wireless Communications
IEEE Journal on Selected Areas in Communications
SIAM Journal on Computing
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We consider a model of next-hop routing by self-interested agents. In this model, nodes in a graph (representing ISPs, Autonomous Systems, etc.) make pricing decisions of how much to charge for forwarding traffic from each of their upstream neighbors, and routing decisions of which downstream neighbors to forward traffic to (i.e., choosing the next hop). Traffic originates at a subset of these nodes that derive a utility when the traffic is routed to its destination node; the traffic demand is elastic and the utility derived from it can be different for different source nodes. Our next-hop routing and pricing model is in sharp contrast with the more common source routing and pricing models, in which the source of traffic determines the entire route from source to destination. For our model, we begin by showing sufficient conditions for prices to result in a Nash equilibrium, and in fact give an efficient algorithm to compute a Nash equilibrium which is as good as the centralized optimum, thus proving that the price of stability is 1. When only a single source node exists, then the price of anarchy is 1 as well, as long as some minor assumptions on player behavior is made. The above results hold for arbitrary convex pricing functions, but with the assumption that the utilities derived from getting traffic to its destination are linear. When utilities can be non-linear functions, we show that Nash equilibrium may not exist, even with simple discrete pricing models.