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Strategic basins of attraction, the farsighted core, and network formation games

By Frank H. Page and Myrna Holtz Wooders

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

Topics: QA, HM
Publisher: University of Warwick, Department of Economics
Year: 2005
OAI identifier: oai:wrap.warwick.ac.uk:1468

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Citations

  1. (2001). 20The farsightedly consistent sets in both versions of this example were computed using a Mathematica package developed by Kamat and Page
  2. (1962). 21A result due to Bondareva
  3. (2001). A Survey of Models of Network Formation: Stability and Efficiency.” doi
  4. (1994). Farsighted Coalitional Stability,” doi
  5. (1996). for an introduction to the partnered core of a nontransferable utility game. 23A famous class of games satisfying this property is assignment, or matching games; see for example Shapley and Shubik
  6. (2001). Group and Network Formation in Industrial Organization; A Survey,” Group Formation doi
  7. (2001). Group Formation; The Interaction of Increasing Returns and Preference Diversity,” doi
  8. (2001). Networks and Markets, The Russel Sage Foundation,
  9. (2001). Strongly Stable Networks,” t y p e s c r i p t ,C a l t e c h ,f o r t h c o m i n gi nGames and Economic Behavior. doi
  10. (1972). The Assignment Game 1; doi
  11. (1996). The partnered core of a game without side payments,” doi
  12. (2001). The Theory of Graphs,D o v e r ,M i n e o l a ,N e wY o r k .( r e p r i n to f the translated French edition published by Dunod,
  13. (1962). Theory of the Core in an n-Person

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