Sharing Costs for Better Selfish Network Design

We consider how to design network cost-sharing protocols to induce benign selfish behavior in large networks. We study this issue in network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of the underlying edge cost-sharing protocols. We seek cost-sharing protocols that minimize the inefficiency of equilibria in the resulting network design game, as measured by the price of anarchy or the price of stability. We delineate between oblivious cost-sharing protocols, where each edge computes cost shares using only “local” information, and the more powerful but less practical class of non-oblivious protocols, where the cost-sharing method of an edge can be informed by the global structure of the network. In undirected networks, even oblivious cost-sharing schemes can dramatically improve the worstcase price of anarchy over that incurred by previously considered schemes. We give nearly matching upper and lower bounds on the worst-case price of anarchy achievable by both oblivious and non-oblivious cost-sharing, in both single-sink and multicommodity networks. In directed networks, simple examples show that non-trivial positive results are possible only for the price of stability. We show that among oblivious cost-sharing protocols, the Shapley cost-sharing scheme minimizes the worst-case price of stability. Conceptually, this result implies that giving edges the ability to identify the identities of its users—as opposed to just the number of users—has no impact on the price of stability, provided only local information is available. We also give results for the price of stability under non-oblivious cost-sharing schemes. Department of Computer Science, Stanford University, 393 Terman Engineering Building, Stanford, CA 94305. Research supported in part by NSF Award 0323766. Email: [email protected]. Department of Computer Science, Stanford University, 462 Gates Building, 353 Serra Mall, Stanford, CA 94305. Supported in part by ONR grant N00014-04-1-0725, DARPA grant W911NF-05-1-0224, and an NSF CAREER Award. Email: [email protected]. Harvard University. Part of this work done while visiting Stanford University and supported in part by DARPA grant W911NF05-1-0224. Email: [email protected].