Abstract
We consider the dynamic network formation problem under the requirement that the whole network be connected and remain connected after q nodes are destroyed. We propose the concept of dynamic Cq-stability and characterize dynamic Cq-stable networks for any q≥0. Comparison with the outcome in the static model is also discussed.
Highlights
The value of a social network relies crucially on its connectivity and resilience, which can be defined by the ability to maintain connectivity even after unexpected trembles due to external shocks.In a prior paper [1], we considered the problem of forming a network under the requirement that the whole network be connected and remain connected after eliminating q nodes, and introduced the concept of the C q -stability of a network in a static setting
The C q -stability is, roughly speaking, to require connectivity in addition to pairwise stability defined by Jackson and Wolinsky [2] even after any at most q nodes are deleted
We extend the network formation problem and the concept of C q -stability to a dynamic setting
Summary
The value of a social network relies crucially on its connectivity and resilience, which can be defined by the ability to maintain connectivity even after unexpected trembles due to external shocks. Haller and Hoyer [6] is a decentralized network formation model just like Jun and Kim [1], but it assumes no information decay, either. It uses the solution concept of Nash stability, whereas Jun and Kim [1]. Our dynamic model of network formation is similar to a sequential version of a network creation game which was introduced by Fabrikant et al [7] Both take the delay cost into account but Fabrikant et al [7] used Nash stability as a solution concept, unlike our paper.
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