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Pairwise-Stability and Nash Equilibria in Network Formation

Listed author(s):
  • Antoni Calvó-Armengol

    (Universitat Autònoma de Barcelona, Université de Toulouse Sciences Sociales and CEPR)

  • Rahmi Ilkiliç

    (Universitat Autònoma de Barcelona)

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
Handle: RePEc:fem:femwpa:2005.34
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  1. Stef Tijs & Anne van den Nouweland & Bhaskar Dutta, 1998. "Link formation in cooperative situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 245-256.
  2. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
  3. 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.
  4. Bloch, Francis & Jackson, Matthew O., 2007. "The formation of networks with transfers among players," Journal of Economic Theory, Elsevier, vol. 133(1), pages 83-110, March.
  5. Mailath, G.J. & Samuelson, L., 1996. "How Proper Is Sequential Equilibrium?," Working papers 9611r, Wisconsin Madison - Social Systems.
  6. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  7. 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, Tilburg University, School of Economics and Management.
  8. Gilles, R.P. & Sarangi, S., 2005. "Stable Networks and Convex Payoffs," Discussion Paper 2005-84, Tilburg University, Center for Economic Research.
  9. Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Francis Bloch & Matthew Jackson, 2006. "Definitions of equilibrium in network formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 305-318, October.
  11. Matthew O. Jackson & Brian W. Rogers, 2005. "Search in the Formation of Large Networks: How Random are Socially Generated Networks?," Game Theory and Information 0503005, EconWPA.
  12. Sanjeev Goyal & Sumit Joshi, 2006. "Unequal connections," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 319-349, October.
  13. 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.
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