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Pairwise-Stability and Nash Equilibria in Network Formation

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  • Antoni Calvó-Armengol
  • Rahmi Ilkiliç

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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Bibliographic Info

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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Keywords: network formation; pairwise-stability; proper equilibrium;

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  1. Mailath, G.J. & Samuelson, L., 1996. "How Proper Is Sequential Equilibrium?," Working papers 9611r, Wisconsin Madison - Social Systems.
  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. 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.
  4. 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.
  5. Dutta, B. & Nouweland, C.G.A.M. van den & Tijs, S.H., 1995. "Link formation in cooperative situations," Discussion Paper 1995-35, Tilburg University, Center for Economic Research.
  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.
  7. 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.
  8. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
    • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  10. Sanjeev Goyal & Sumit Joshi, 2006. "Unequal connections," International Journal of Game Theory, Springer, vol. 34(3), pages 319-349, October.
  11. Sudipta Sarangi & Robert P. Gilles, . "Stable Networks and Convex Payoffs," Departmental Working Papers 2005-13, Department of Economics, Louisiana State University.
  12. 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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