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Pairwise-Stability and Nash Equilibria in Network Formation

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Author Info
Antoni Calvó-Armengol (Universitat Autònoma de Barcelona, Université de Toulouse Sciences Sociales and CEPR)
Rahmi Ilkiliç (Universitat Autònoma de Barcelona)

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Abstract

Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks.

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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2005.34.

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Date of creation: Mar 2005
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Handle: RePEc:fem:femwpa:2005.34

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Related research
Keywords: Network formation; Pairwise-stability; Proper equilibrium;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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References listed on IDEAS
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  1. Francis Bloch & Matthew Jackson, 2006. "Definitions of equilibrium in network formation games," International Journal of Game Theory, Springer, vol. 34(3), pages 305-318, October. [Downloadable!] (restricted)
  2. repec:att:wimass:199611 is not listed on IDEAS
  3. Sudipta Sarangi & Robert P. Gilles, . "Stable Networks and Convex Payoffs," Departmental Working Papers 2005-13, Department of Economics, Louisiana State University. [Downloadable!]
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  4. Bloch, Francis & Jackson, Matthew, 2004. "The Formation of Networks with Transfers among Players," Working Papers 1194, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  5. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  6. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October. [Downloadable!] (restricted)
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  7. Bhaskar Dutta & Suresh Mutuswami, 1997. "Stable Networks," Tinbergen Institute Discussion Papers 97-039/1, Tinbergen Institute.
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  8. Stef Tijs & Anne van den Nouweland & Bhaskar Dutta, 1998. "Link formation in cooperative situations," International Journal of Game Theory, Springer, vol. 27(2), pages 245-256. [Downloadable!] (restricted)
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  9. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May. [Downloadable!] (restricted)
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  10. Sanjeev Goyal & Sumit Joshi, 2006. "Unequal connections," International Journal of Game Theory, Springer, vol. 34(3), pages 319-349, October. [Downloadable!] (restricted)
  11. Mailath, George J. & Samuelson, Larry & Swinkels, Jeroen M., 1997. "How Proper Is Sequential Equilibrium?," Games and Economic Behavior, Elsevier, vol. 18(2), pages 193-218, February. [Downloadable!] (restricted)
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  12. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Marco A. Marini, 2007. "An Overview of Coalitions and Networks Formation Models for Economic Applications," Working Papers 0707, CREI Università degli Studi Roma Tre, revised 2007. [Downloadable!]
  2. Carlos Pimienta, 2007. "Generic Determinacy of Nash Equilibrium in Network Formation Games," Discussion Papers 2007-31, School of Economics, The University of New South Wales. [Downloadable!]
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  3. Frank Page & Myrna Wooders, 2007. "Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games," Caepr Working Papers 2007-020, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington. [Downloadable!]
    Other versions:
  4. Chantarat, Sommarat & Barrett, Christopher B., 2007. "Social Network Capital, Economic Mobility and Poverty Traps," MPRA Paper 1947, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  5. Marco Marini, 2007. "An Overview of Coalition & Network Formation Models for Economic Applications," Working Papers 0712, University of Urbino Carlo Bo, Department of Economics, revised 2007. [Downloadable!]
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