Networks and farsighted stability
Networks and Farsighted Stability By Frank H. Page, Jr. Department of Finance University of Alabama Tuscaloosa, AL 35487 USA firstname.lastname@example.org Myrna H. Wooders Department of Economics University of Warwick Coventry CV4 7AL UK M.Wooders@warwick.ac.uk Samir Kamat Portfolio Management Group Wachovia Corporation Atlanta, GA 30303 USA email@example.com The main contribution of this paper is to provide a framework in which the notion of farsighted stability for games, introduced by Chwe (1994), can be applied to directed networks. In particular, we introduce the notion of a supernetwork. A supernetwork is made up of a collection of directed networks (the nodes) and uniquely represents (via the arcs connecting the nodes) agent preferences and the rules governing network formation. By reformulating Chwe's basic result on the nonemptiness of farsightedly stable sets, we show that for any supernetwork (i.e., for any collection of directed networks and any collection of rules governing network formation), there exists a farsightedly stable directed network. We also introduce the notion of a Nash network relative to a given supernetwork, as well as the notions of symmetric, nonsimultaneous, and decomposable supernetworks. To illustrate the utility of our framework, we present several examples of supernetworks, compute the farsightedly stable networks, and the Nash networks.
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