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Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games

37 Pages Posted: 4 Oct 2007  

Frank H. Page Jr.

Indiana University, Bloomington - Department of Economics; Systemic Risk Centre, LSE

Myrna H. Wooders

Vanderbilt University - College of Arts and Science - Department of Economics

Date Written: October 4, 2007

Abstract

Given the preferences of players and the rules governing network formation, what networks are likely to emerge and persist? And how do individuals and coalitions evaluate possible consequences of their actions in forming networks? To address these questions we introduce a model of network formation whose primitives consist of a feasible set of networks, player preferences, the rules of network formation, and a dominance relation on feasible networks. The rules of network formation may range from non-cooperative, where players may only act unilaterally, to cooperative, where coalitions of players may act in concert. The dominance relation over feasible networks incorporates not only player preferences and the rules of network formation but also assumptions concerning the degree of farsightedness of players. A specification of the primitives induces an abstract game consisting of (i) a feasible set of networks, and (ii) a path dominance relation defined on the feasible set of networks. Using this induced game we characterize sets of network outcomes that are likely to emerge and persist. Finally, we apply our approach and results to characterize the equilibrium of well known models and their rules of network formation, such as those of Jackson and Wolinsky (1996) and Jackson and van den Nouweland (2005).

Keywords: basins of attraction, network formation games, stable sets, path dominance core, Nash networks

JEL Classification: A14, C71, C72

Suggested Citation

Page, Frank H. and Wooders, Myrna H., Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games (October 4, 2007). CAEPR Working Paper No. 2007-020. Available at SSRN: https://ssrn.com/abstract=1019244 or http://dx.doi.org/10.2139/ssrn.1019244

Frank H. Page Jr. (Contact Author)

Indiana University, Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

Systemic Risk Centre, LSE ( email )

Houghton St
London, WC2A 2AE
United Kingdom

HOME PAGE: http://www.systemicrisk.ac.uk/

Myrna H. Wooders

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

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