Stability of Networks Under Level-K Farsightedness

41 Pages Posted: 30 Aug 2014

See all articles by P. Jean-Jacques Herings

P. Jean-Jacques Herings

Maastricht University

Ana Mauleon

Université Saint-Louis - Bruxelles; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Vincent J. Vannetelbosch

Center for Operations Research and Econometrics (CORE)

Date Written: July 10, 2014

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.

Keywords: Farsightedness, Stability, Networks

JEL Classification: A14, C70, D20

Suggested Citation

Herings, P. Jean-Jacques and Mauleon Echeverria, Ana Carmen and Vannetelbosch, Vincent J., Stability of Networks Under Level-K Farsightedness (July 10, 2014). Available at SSRN: https://ssrn.com/abstract=2488995 or http://dx.doi.org/10.2139/ssrn.2488995

P. Jean-Jacques Herings (Contact Author)

Maastricht University ( email )

Department of Economics
P.O. Box 616
6200 MD Maastricht
Netherlands
+31 43 3883636 (Phone)
+31 43 3884878 (Fax)

HOME PAGE: http://www.personeel.unimaas.nl/p.herings/herings.htm

Ana Carmen Mauleon Echeverria

Université Saint-Louis - Bruxelles ( email )

Brussels, 1000
Belgium

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Vincent J. Vannetelbosch

Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
1348 Louvain-la-Neuve, 1348
Belgium

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