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Generic Determinacy of Nash Equilibrium in Network Formation Games

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  • Carlos Pimienta

    (School of Economics, The University of New South Wales)

Abstract

This paper shows that the set of probability distributions over networks induced by Nash equilibria of the network formation game proposed by Myerson (1991) is finite for a generic assignment of payoffs to networks. The same result can be extended to several variations of the game found in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:swe:wpaper:2007-31
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    File URL: http://wwwdocs.fce.unsw.edu.au/economics/Research/WorkingPapers/2007_31.pdf
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    References listed on IDEAS

    as
    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Kukushkin, Nikolai S. & Litan, Cristian M. & Marhuenda, Francisco, 2008. "On the generic finiteness of equilibrium outcome distributions in bimatrix game forms," Journal of Economic Theory, Elsevier, vol. 139(1), pages 392-395, March.
    3. Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 51-79, March.
    4. De Sinopoli, Francesco, 2001. "On the Generic Finiteness of Equilibrium Outcomes in Plurality Games," Games and Economic Behavior, Elsevier, vol. 34(2), pages 270-286, February.
    5. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    6. 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.
    7. Park, In-Uck, 1997. "Generic Finiteness of Equilibrium Outcome Distributions for Sender-Receiver Cheap-Talk Games," Journal of Economic Theory, Elsevier, vol. 76(2), pages 431-448, October.
    8. Kukushkin, Nicolai S. & Litan, Cristian M., 2007. "On the generic finiteness of outcome distributions for bimatrix game forms," UC3M Working papers. Economics we073520, Universidad Carlos III de Madrid. Departamento de Economía.
    9. Govindan, Srihari & McLennan, Andrew, 2001. "On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms," Econometrica, Econometric Society, vol. 69(2), pages 455-471, March.
    10. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    11. Francesco Sinopoli & Giovanna Iannantuoni, 2005. "On the generic strategic stability of Nash equilibria if voting is costly," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(2), pages 477-486, February.
    12. Matthew O. Jackson, 2003. "A Survey of Models of Network Formation: Stability and Efficiency," Game Theory and Information 0303011, University Library of Munich, Germany.
    13. Calvo-Armengol, Antoni, 2004. "Job contact networks," Journal of Economic Theory, Elsevier, vol. 115(1), pages 191-206, March.
    14. 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.
    15. Rachel E. Kranton & Deborah F. Minehart, 2001. "A Theory of Buyer-Seller Networks," American Economic Review, American Economic Association, vol. 91(3), pages 485-508, June.
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    Citations

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    Cited by:

    1. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    2. Bich, Philippe & Fixary, Julien, 2022. "Network formation and pairwise stability: A new oddness theorem," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    3. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03287524, HAL.
    4. Pimienta, Carlos, 2010. "Generic finiteness of outcome distributions for two-person game forms with three outcomes," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 364-365, May.
    5. De Sinopoli, Francesco & Pimienta, Carlos, 2010. "Costly network formation and regular equilibria," Games and Economic Behavior, Elsevier, vol. 69(2), pages 492-497, July.
    6. Bich, Philippe & Fixary, Julien, 2024. "Oddness of the number of Nash equilibria: The case of polynomial payoff functions," Games and Economic Behavior, Elsevier, vol. 145(C), pages 510-525.
    7. Philippe Bich & Julien Fixary, 2021. "Oddness of the number of Nash equilibria: the case of polynomial payoff functions," Post-Print halshs-03354269, HAL.
    8. Philippe Bich & Julien Fixary, 2021. "Oddness of the number of Nash equilibria: the Case of Polynomial Payoff Functions," Documents de travail du Centre d'Economie de la Sorbonne 21027, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Post-Print halshs-03287524, HAL.
    10. Philippe Bich & Julien Fixary, 2021. "Oddness of the number of Nash equilibria: the case of polynomial payoff functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03354269, HAL.

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    More about this item

    Keywords

    Networks; generic finiteness; Nash Equilibrium;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - 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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