Stability of networks under level-k farsightedness

P. Jean-Jacques Herings, Ana Mauleon and Vincent Vannetelbosch

No 30, Research Memorandum from Maastricht University, Graduate School of Business and Economics (GSBE)

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.

Date: 2014-01-01
New Economics Papers: this item is included in nep-gth and nep-mic
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Citations: View citations in EconPapers (8)

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Working Paper: Stability of networks under level-K farsightedness (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:unm:umagsb:2014030

DOI: 10.26481/umagsb.2014030

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