Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games

36 Pages Posted: 16 Mar 2005  

Frank H. Page

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: March 2005

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-Morgenstern stable set as a farsighted basis. (4) The core of the farsighted network formation game 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 at least 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 the farsighted core is contained in the set of pairwise stable networks. Finally, we introduce, via an example, competitive contracting networks and highlight how the analysis of these networks requires the new features of our network formation model.

Keywords: Basins of attraction, Network formation, Supernetworks, Farsighted core, Nash networks

JEL Classification: A14, D20, J00

Suggested Citation

Page, Frank H. and Wooders, Myrna H., Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games (March 2005). FEEM Working Paper No. 36.05. Available at SSRN: https://ssrn.com/abstract=681263 or http://dx.doi.org/10.2139/ssrn.681263

Frank H. Page (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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