Networks and farsighted stability
Page, Frank H., Wooders, Myrna Holtz and Kamat, Samir (2002) Networks and farsighted stability. Working Paper. Covnetry: University of Warwick, Department of Economics. (Warwick economic research papers).
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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 super-networks, compute the farsightedly stable networks, and the Nash networks.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HD Industries. Land use. Labor
H Social Sciences > HM Sociology
|Divisions:||Faculty of Social Sciences > Economics|
|Library of Congress Subject Headings (LCSH):||Business networks, Organizational sociology, Economics -- Sociological aspects, Organizational behavior, Social stability|
|Series Name:||Warwick economic research papers|
|Publisher:||University of Warwick, Department of Economics|
|Place of Publication:||Covnetry|
|Number of Pages:||34|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Description:||Original version, July 2001, this version, November 2002.|
|Adapted As:||Page, F.H., Wooders, M.H. and Kamat, S. (2003). Networks and Farsighted Stability. [Coventry] : University of Warwick, Economics Department. (Warwick economic research papers, no.689).|
|Version or Related Resource:||Revised version of: Page, F.H., Wooders, M.H. and Kamat, S. (2001). Networks and Farsighted Stability. [Coventry] : University of Warwick, Economics Department. (Warwick economic research papers, no.621).|
|References:|| Bala, V. and S. Goyal (2000) “A Noncooperative Model of Network Formation,” Econometrica 68, 1181-1229.  Chwe, M. (1994) “Farsighted Coalitional Stability,” Journal of Economic Theory 63, 299-325.  Dutta, B. and S. Mutuswami (1997) “Stable Networks,” Journal of Economic Theory 76, 322-344.  Jackson, M. O. (2001) “The Stability and E¢ciency of Economic and Social Networks,” typescript, Caltech.  Jackson, M. O. and A. van den Nouweland (2001) “Strongly Stable Networks,” typescript, Caltech.  Jackson, M. O. and A. Watts (2001) “The Evolution of Social and Economic Networks,” Caltech Working Paper 1044.  Jackson, M. O. and A. Wolinsky (1996) “A Strategic Model of Social and Economic Networks,” Journal of Economic Theory 71, 44-74.  Konishi, H. and D. Ray (2001) “Coalition Formation as a Dynamic Process,” typescript, New York University.  Kamat, S. and F. H. Page, Jr. “Computing Farsighted Stable Sets,” typescript, University of Alabama.  Rockafellar, R. T. (1984) Network Flows and Monotropic Optimization, John Wiley & Sons Inc., New York.  Shapley, L. S. and M. Shubik (1969) “On the Core of an Economic System with Externalities,” American Economic Review 59, 678-684.  Skyrms, B. and R. Pemantle (2000) “A Dynamic Model of Social Network Formation,” Proceedings of the National Academy of Sciences, 97, 9340-9346.  Slikker, M. and A. van den Nouweland (2001) Social and Economic Networks in Cooperative Game Theory, Kluwer, The Netherlands.  Watts, A. (2001) “A Dynamic Model of Network Formation,” Games and Economic Behavior, 34, 331-341.|
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