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

Frank Page and Myrna Wooders

No 509, Vanderbilt University Department of Economics Working Papers from Vanderbilt University Department of Economics

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. ÊÊÊÊÊÊÊÊ 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: Networks; basin of attraction; farsighted core; network formation; strategic basins of attraction (search for similar items in EconPapers)
JEL-codes: C71 C72 (search for similar items in EconPapers)
Date: 2005-04
New Economics Papers: this item is included in nep-gth and nep-net
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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Related works:
Working Paper: Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games (2005)
Working Paper: Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games (2005)
Working Paper: Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:van:wpaper:0509

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