a characterization of farsightedly stable networks思索稳定网络的一个特征.pdfVIP

Games 2010, 1, 226-241; doi:10.3390/g1030226 OPEN ACCESS games ISSN 2073-4336 /journal/games Article A Characterization of Farsightedly Stable Networks Gilles Grandjean , Ana Mauleon and Vincent Vannetelbosch ´ CORE, Universite catholique de Louvain, 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium; E-Mail: gilles.grandjean@uclouvain.be ´ FNRS and CEREC, Facultes universitaires Saint-Louis, 43 Boulevard du Jardin Botanique, 1000 Brussels, Belgium; E-Mail: Mauleon@fusl.ac.be ´ FNRS and CORE, Universite catholique de Louvain, 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium Author to whom correspondence should be addressed; E-Mail: vincent.vannetelbosch@uclouvain.be; Tel.: +32-10-474142; Fax: +32-10-474301. Received: 4 June 2010; in revised form: 7 July 2010 / Accepted: 16 July 2010 / Published: 22 July 2010 Abstract: We study the stability of social and economic networks when players are farsighted. We first provide an algorithm that characterizes the unique pairwise and groupwise farsightedly stable set of networks under the componentwise egalitarian allocation rule. We then show that this set coincides with the unique groupwise myopically stable set of networks but not with the unique pairwise myopically stable set of networks. We conclude that, if groupwise deviations are allowed then whether players are farsighted or myopic does not matter; if players are farsighted then whether players are allowed to deviat