A Characterization of Farsightedly Stable Networks

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

Competition and networks of collaboration

“…Several papers in this literature follow a cooperative approach and use farsighted stability concepts as solutions. This strand of the literature includes Greenberg (), Chwe (), Ray and Vohra (), Diamantoudi and Xue (), Herings et al (), Page et al (), Grandjean et al (, ), and Mauleon et al (). The version of the farsighted stable set used in this paper differs from the versions defined in the above papers in a few aspects.…”

“…First, I allow for arbitrary acting coalitions ( Herings et al 2009 and Mauleon et al 2011 restrict the acting coalition to be a singleton or a pair). Second, I allow agents to choose all of their actions (i.e., the intensity of collaboration and the sizes of transfers) in a cooperative manner ( Herings et al 2009 , Page et al 2005 , Grandjean et al 2010 , , and Mauleon et al 2011 focus on pure network formation).…”