Stability of networks under level-k farsightedness

P.J.J. Herings, A. Mauleon, V. Vannetelbosch

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Abstract

We provide a tractable concept that can be used to study the influence of the degree of farsightedness on network stability. A set of networks GK is a level-K farsightedly stable set if three conditions are satisfied. First, external deviations should be deterred. Second, from any network outside of GK there is a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in GK. Third, there is no proper subset of GK satisfying the first two conditions.
We show that a level-K farsightedly stable set always exists and we provide a sufficient condition for the uniqueness of a level-K farsightedly stable set. There is a unique level-1 farsightedly stable set G1 consisting of all networks that belong to closed cycles. Level-K farsighted stability leads to a refinement of G1 for generic allocation rules. We then provide easy to verify conditions for a set to be level-K farsightedly stable and we consider the relationship between level-K farsighted stability and efficiency of networks. We show the tractability of the concept by applying it to a model of criminal networks.
Original languageEnglish
Place of PublicationMaastricht
PublisherMaastricht University, Graduate School of Business and Economics
DOIs
Publication statusPublished - 1 Jan 2014

Publication series

SeriesGSBE Research Memoranda
Number030

Cite this

Herings, P. J. J., Mauleon, A., & Vannetelbosch, V. (2014). Stability of networks under level-k farsightedness. Maastricht University, Graduate School of Business and Economics. GSBE Research Memoranda, No. 030 https://doi.org/10.26481/umagsb.2014030