Page, Frank H. and Wooders, Myrna Holtz (2005) Strategic basins of attraction, the farsighted core, and network formation games. Working Paper. University of Warwick, Department of Economics, Coventry.

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Abstract

We make four main contributions to the theory of network formation. (1) The problem of network formation with farsighted agents can be formulated as an abstract network formation game. (2) In any farsighted network formation game the feasible set of networks contains a unique, finite, disjoint collection of nonempty subsets having the property that each subset forms a strategic basin of attraction. These basins of attraction contain all the networks that are likely to emerge and persist if individuals behave farsightedly in playing the network formation game. (3) A von Neumann Morgenstern stable set of the farsighted network formation game is constructed by selecting one network from each basin of attraction. We refer to any such von Neumann-Morgebstern stable set as farsighted basis. (4) The core of the farsighted network formation games is constructed by selecting one network from each basin of attraction containing a single network. We call this notion of the core, the farsighted core. We conclude that the farsighted core is nonempty if and only if there exists one farsighted basin of attraction containing a single network. To relate our three equilibrium and stability notions (basins of attraction, farsighted basis and farsighted core) to recent work by Jackson and Wolinsky (1996), we define a notion of pairwise stability similar to the Jackson-Wolinsky notion and we show that a farsighted core is contained in the set of pairwise stable networks. Finally, we introduce, via an example, competitative contracting networks and highlight how the analysis of these networks requires the new features of our network formation model.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics H Social Sciences > HM Sociology
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Economics -- Sociological aspects, Social networks, Attractors (Mathematics), Differentiable dynamical systems, Labor economics, Production functions (Economic theory)
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	March 2005
Number:	No.724
Number of Pages:	37
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Available As:	Page, F.H. and Wooders, M.H. (2005). Strategic basins of attraction, the farsighted core, and network formation games. Milano : Fondazione Eni Enrico Mattei. (FEEM working paper, no.36.05)
References:	[1] Berge, C. (2001) The Theory of Graphs, Dover, Mineola, New York. (reprint of the translated French edition published by Dunod, Paris, 1958). [2] Bloch, F. (2001) “Group and Network Formation in Industrial Organization; A Survey,” Group Formation in Economics: Networks, Clubs, and Coalitions, G. Demange and M. Wooders (eds.). Cambridge University Press, forthcoming. [3] Bondareva, O. (1962) “Theory of the Core in an n-Person Game,” Vestnik, LGU13, 141-142 (in Russian), (Leningrad State University, Leningrad). [4] Casella, A. and J. Rauch (2001) Networks and Markets, The Russel Sage Foundation, New York. [5] Chwe, M. (1994) “Farsighted Coalitional Stability,” Journal of Economic Theory 63, pp. 299-325. [6] Demange, G. (2001) “Group Formation; The Interaction of Increasing Returns and Preference Diversity,” In: Demange, G. and M. H. Wooders. (eds.) Group Formation in Economics: Networks, Clubs, and Coalitions. Cambridge University Press, forthcoming. [7] Jackson, M. O. (2001) “A Survey of Models of Network Formation: Stability and Efficiency.” In: Demange, G. and M. H. Wooders. (eds.) Group Formation in Economics: Networks, Clubs, and Coalitions. Cambridge University Press, forthcoming. [8] Jackson, M. O. and A. van den Nouweland (2001) “Strongly Stable Networks,” typescript, Caltech, forthcoming in Games and Economic Behavior. [9] Jackson, M. O. and A. Watts (2001) “The Evolution of Social and Economic Networks,” Journal of Economic Theory 106, pp. 265-295. [10] Jackson, M. O. and A. Wolinsky (1996) “A Strategic Model of Social and Economic Networks,” Journal of Economic Theory 71, pp. 44-74. [11] Kamat, S. and F. H. Page, Jr. (2001) “Computing Farsighted Stable Sets,” typescript, University of Alabama. [12] Page, Jr., F. H., M. H. Wooders and S. Kamat (2001) “Networks and Farsighted Stability,” Warwick Economic Research Papers, No 621, University of Warwick, forthcoming in the Journal of Economic Theory. [13] Reny, P.J. and M.H. Wooders (1996) “The partnered core of a game without side payments,” Journal of Economic Theory 70, 298-311. [14] Scarf, H. (1967) “The Core of an n-person Game,” Econometrica 35, 50-69. [15] Shapley, L. S.. and M. Shubik (1972) “The Assignment Game 1; The Core,” International Journal of Game Theory 1, 11-30.
URI:	http://wrap.warwick.ac.uk/id/eprint/1468

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