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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. Dutta, B. & van den Nouweland, C.G.A.M. & Tijs, S.H., 1998. "Link formation in cooperative situations," Other publications TiSEM fb302bdf-f6ab-4909-99d5-5, Tilburg University, School of Economics and Management.
  2. 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.
  3. 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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  6. Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  8. George J. Mailath & Larry Samuelson & Jeroen M. Swinkels, . "How Proper is Sequential Equilibrium," ELSE working papers 045, ESRC Centre on Economics Learning and Social Evolution.
  9. 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.
  10. 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.
  11. 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.
  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.
  13. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
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