Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
The Largest Eigenvalue of Sparse Random Graphs
Combinatorics, Probability and Computing
The largest eigenvalue of nonregular graphs
Journal of Combinatorial Theory Series B
Comparing economic incentives in peer-to-peer networks
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Internet economics: Pricing and policies
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Strategic formation of credit networks
Proceedings of the 21st international conference on World Wide Web
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We consider a stylized model of content contribution in a peer-to-peer network. The model is appealing because it allows for linear-quadratic payoff functions and for very general interaction patterns among agents. Furthermore, when the model has a unique Nash equilibrium (NE) we find that it is defined by a network centrality measure (Bonacich 1987), with L1 and L2 norms of the Bonacich index vector providing aggregate contribution and social welfare. Furthermore, we find that NE are always (even when they are non-unique) computable by solving a linear complementarity problem. We study the network designer's problem of engineering the most efficient equilibrium outcome, proving that maximizing aggregate contribution can be reconciled with maximizing aggregate welfare. We also provide a partial characterization of optimal NE graphs and suggest different approaches for how a network designer can promote more efficient graph structures.