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Pairwise-Stability and Nash Equilibria in Network Formation

  • Antoni Calvó-Armengol
  • Rahmi Ilkiliç

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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File URL: http://research.barcelonagse.eu/tmp/working_papers/182.pdf
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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 182.

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Date of creation: Apr 2004
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Handle: RePEc:bge:wpaper:182
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  1. Mailath, G.J. & Samuelson, L., 1996. "How Proper Is Sequential Equilibrium?," Working papers 9611r, Wisconsin Madison - Social Systems.
  2. Matthew O. Jackson, 2001. "Strongly Stable Networks," University of Oregon Economics Department Working Papers 2001-3, University of Oregon Economics Department, revised 15 Nov 2002.
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    • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
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  5. 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.
  6. 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.
  7. Sudipta Sarangi & Robert P. Gilles, . "Stable Networks and Convex Payoffs," Departmental Working Papers 2005-13, Department of Economics, Louisiana State University.
  8. Jackson, Matthew O. & Rogers, Brian W., 2005. "Search in the formation of large networks: How random are socially generated networks?," Working Papers 1216, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. repec:dgr:kubcen:200584 is not listed on IDEAS
  10. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Matthew O. Jackson & Francis Bloch, 2004. "The Formation of Networks with Transfers among Players," Working Papers 2004.80, Fondazione Eni Enrico Mattei.
  12. Sanjeev Goyal & Sumit Joshi, 2006. "Unequal connections," International Journal of Game Theory, Springer, vol. 34(3), pages 319-349, October.
  13. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, School of Economics and Management.
  14. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  15. 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.
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