Grandjean, Gilles; Mauleon, Ana; Vannetelbosch, Vincent A characterization of farsightedly stable networks. (English) Zbl 1311.91166 Games 1, No. 3, 226-241 (2010). Summary: 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. Cited in 1 Document MSC: 91D30 Social networks; opinion dynamics 91A43 Games involving graphs Keywords:farsighted players; pairwise deviations; groupwise deviations PDFBibTeX XMLCite \textit{G. Grandjean} et al., Games 1, No. 3, 226--241 (2010; Zbl 1311.91166) Full Text: DOI References: [1] Jackson, The stability and efficiency of economic and social networks, Networks and Groups: Models of Strategic Formation pp 99– (2003) [2] Jackson, A survey of models of network formation: Stability and efficiency, Group Formation in Economics: Networks, Clubs and Coalitions pp 11– (2005) [3] Jackson, Social and Economic Networks (2008) [4] Goyal, Connections: An Introduction to the Economics of Networks (2007) · Zbl 1138.91005 [5] DOI: 10.1006/jeth.1996.0108 · Zbl 0871.90144 · doi:10.1006/jeth.1996.0108 [6] DOI: 10.1016/j.geb.2008.12.009 · Zbl 1188.91186 · doi:10.1016/j.geb.2008.12.009 [7] DOI: 10.1006/jeth.1994.1044 · Zbl 0841.90131 · doi:10.1006/jeth.1994.1044 [8] DOI: 10.1007/s001990050204 · Zbl 0903.90005 · doi:10.1007/s001990050204 [9] DOI: 10.1016/j.geb.2003.11.003 · Zbl 1099.91020 · doi:10.1016/j.geb.2003.11.003 [10] DOI: 10.1007/s11238-004-2646-1 · Zbl 1090.91009 · doi:10.1007/s11238-004-2646-1 [11] DOI: 10.1016/j.jet.2004.05.001 · Zbl 1112.91013 · doi:10.1016/j.jet.2004.05.001 [12] DOI: 10.1016/j.jet.2004.02.007 · Zbl 1097.90012 · doi:10.1016/j.jet.2004.02.007 [13] DOI: 10.1016/j.geb.2008.05.003 · Zbl 1161.91334 · doi:10.1016/j.geb.2008.05.003 [14] DOI: 10.1016/j.geb.2004.08.004 · Zbl 1099.91011 · doi:10.1016/j.geb.2004.08.004 [15] DOI: 10.1006/jeth.2001.2903 · Zbl 1099.91543 · doi:10.1006/jeth.2001.2903 [16] DOI: 10.1006/jeth.1997.2306 · Zbl 0893.90043 · doi:10.1006/jeth.1997.2306 [17] Banerjee, Efficiency and stability in economic networks, Mimeo (1999) [18] Von Neumann, Theory of Games and Economic Behavior (1944) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.