Stability of Networks under Limited Farsightedness
(2014) Second Bordeaux Workshop on Economic Theory, Design and Games — Location: Université de Bordeaux, Bordeaux, France (26.May.2014)
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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 G_{K} is a level-K farsightedly stable set if three conditions are satisfied. First, external deviations should be deterred. Second, from any network outside of G_{K} there is a a sequence of farsighted improving paths of length smaller than or equal to K leading to some network in G_{K}. Third, there is no proper subset of G_{K} 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 limited farsighted stability and efficiency of networks.
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Mauleon, A. (2014). Stability of Networks under Limited Farsightedness. Second Bordeaux Workshop on Economic Theory, Design and Games, Université de Bordeaux, Bordeaux, France. https://hdl.handle.net/2078.5/199025