Farsightedly stable networks

We propose a new concept, pairwise farsighted stable set, in order to predict which networks may be formed among farsighted players. A set of networks G is pairwise farsighted stable (i) if all possible pairwise deviations from any network g ∈ G are deterred by the threat of ending worse off or equal off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). We show that a pairwise farsighted stable set always exists and we provide the necessary and sufficient condition such that a unique pairwise farsighted stable set consisting of a single network exists. We find that the pairwise farsighted stable sets and the set of strongly efficient networks, those which are socially optimal, may be disjoint if the allocation rules have nice properties. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest consistent set. ∗Vincent Vannetelbosch and Ana Mauleon are Research Associates of the National Fund for Scientific Research (FNRS). Vincent Vannetelbosch is Associate Fellow of CEREC, Facultés Universitaires SaintLouis. Financial support from the research project BEC 2003-02084 (Universidad del Pais Vasco) funded by the Spanish government and from the Belgian French Community’s programs Action de Recherches Concertée 03/08-302 and 05/10-331 (UCL) is gratefully acknowledged. Corresponding author: Prof. Vincent Vannetelbosch, CORE, University of Louvain, 34 voie du Roman Pays, B-1348 Louvain-la-Neuve, Belgium. E-mail: [email protected].