Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games
AbstractWe 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.
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Bibliographic InfoPaper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 724.
Length: 37 pages
Date of creation: 2005
Date of revision:
Basins of attraction ; Network formation ; Supernetworks ; Farsighted core ; Nash networks;
Other versions of this item:
- Frank H. Page, Jr. & Myrna H. Wooders, 2005. "Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games," Vanderbilt University Department of Economics Working Papers 0509, Vanderbilt University Department of Economics.
- Frank H. Page, Jr. & Myrna H. Wooders, 2005. "Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games," Working Papers 2005.36, Fondazione Eni Enrico Mattei.
- A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
- D20 - Microeconomics - - Production and Organizations - - - General
- J00 - Labor and Demographic Economics - - General - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-06-10 (All new papers)
- NEP-GTH-2006-06-10 (Game Theory)
- NEP-MIC-2006-06-10 (Microeconomics)
- NEP-NET-2006-06-10 (Network Economics)
- NEP-SOC-2006-06-10 (Social Norms & Social Capital)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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