Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Toward a Containment Strategy for Smallpox Bioterror: An Individual-Based Computational Approach
Toward a Containment Strategy for Smallpox Bioterror: An Individual-Based Computational Approach
Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics)
Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics)
Social and Economic Networks
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There are a number of domains where agents must collectively form a network in the face of the following trade-off: each agent receives benefits from the direct links it forms to others, but these links expose it to the risk of being hit by a cascading failure that might spread over multistep paths. Financial contagion, epidemic disease, the exposure of covert organizations to discovery, and electrical power networks are all settings in which such issues have been articulated. Here we formulate the problem in terms of strategic network formation, and provide asymptotically tight bounds on the welfare of both optimal and stable networks. We find that socially optimal networks are, in a precise sense, situated just beyond a phase transition in the behavior of the cascading failures, and that stable graphs lie slightly further beyond this phase transition, at a point where most of the available welfare has been lost. Our analysis enables us to explore such issues as the trade-offs between clustered and anonymous market structures, and it exposes a fundamental sense in which very small amounts of “over-linking” in networks with contagious risk can have strong consequences for the welfare of the participants.