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• Mauleon, A
• Vannetelbosch, V
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• Mauleon, A
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• Mauleon, A
• Vannetelbosch, V

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Games 2010, 1(3), 226-241; doi:10.3390/g1030226

Article

A Characterization of Farsightedly Stable Networks

Gilles Grandjean ¹ , Ana Mauleon ^2,3  and Vincent Vannetelbosch ^3,*

¹ CORE, Université catholique de Louvain, 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium ² FNRS and CEREC, Facultés universitaires Saint-Louis, 43 Boulevard du Jardin Botanique, 1000 Brussels, Belgium ³ FNRS and CORE, Université catholique de Louvain, 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium

* Author to whom correspondence should be addressed.

Received: 4 June 2010; in revised form: 7 July 2010 / Accepted: 16 July 2010 / Published: 22 July 2010

(This article belongs to the Special Issue Social Networks and Network Formation)

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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 deviate in pairs only or in groups does not matter.

Keywords: farsighted players; pairwise deviations; groupwise deviations

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