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Pairwise-stability and Nash equilibria in network formation

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  • Antoni Calvó-Armengol
  • Rahmi İlkılıç

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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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Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:38:y:2009:i:1:p:51-79 DOI: 10.1007/s00182-008-0140-7
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    References listed on IDEAS

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    Cited by:

    1. Pimienta, Carlos, 2009. "Generic determinacy of Nash equilibrium in network-formation games," Games and Economic Behavior, Elsevier, vol. 66(2), pages 920-927, July.
    2. Dev, Pritha, 2014. "Identity and fragmentation in networks," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 86-100.
    3. Sommarat Chantarat & Christopher Barrett, 2012. "Social network capital, economic mobility and poverty traps," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, pages 299-342.
    4. Gilles, R.P. & Sarangi, S., 2005. "Stable Networks and Convex Payoffs," Discussion Paper 2005-84, Tilburg University, Center for Economic Research.
    5. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    6. Maia Güell & José V. Rodríguez Mora & Christopher I. Telmer, 2015. "The Informational Content of Surnames, the Evolution of Intergenerational Mobility, and Assortative Mating," Review of Economic Studies, Oxford University Press, pages 693-735.
    7. Seungmoon Choi & Virginie Masson & Angus Moore & Mandar Oak, 2013. "Networks and Favor Exchange Norms under Stochastic Costs," School of Economics Working Papers 2013-04, University of Adelaide, School of Economics.
    8. Tim Hellmann & Berno Buechel, 2009. "Under-connected and Over-connected Networks," Working Papers 2009.38, Fondazione Eni Enrico Mattei.
    9. Saitis, Athanasios, 2013. "Kartellbekämpfung und interne Kartellstrukturen: Ein netzwerktheoretischer Ansatz," FZID Discussion Papers 85-2013, University of Hohenheim, Center for Research on Innovation and Services (FZID).
    10. Antonio Cabrales & Piero Gottardi & Fernando Vega-Redondo, 2017. "Risk Sharing and Contagion in Networks," Review of Financial Studies, Society for Financial Studies, pages 3086-3127.
    11. Buechel, Berno, 2011. "Network formation with closeness incentives," Center for Mathematical Economics Working Papers 395, Center for Mathematical Economics, Bielefeld University.
    12. Lasse Kliemann, 2011. "The Price of Anarchy for Network Formation in an Adversary Model," Games, MDPI, Open Access Journal, vol. 2(3), pages 1-31, August.
    13. William Kerr & Ufuk Akcigit & Nicholas Bloom & Daron Acemoglu, 2012. "Innovation, Reallocation and Growth," 2012 Meeting Papers 1137, Society for Economic Dynamics.
    14. Zenou, Yves, 2011. "Search, migration, and urban land use: The case of transportation policies," Journal of Development Economics, Elsevier, vol. 96(2), pages 174-187, November.
    15. Attila Ambrus & Arun G. Chandrasekhar & Matt Elliott, 2014. "Social Investments, Informal Risk Sharing, and Inequality," NBER Working Papers 20669, National Bureau of Economic Research, Inc.
    16. Michael Caldara & Michael McBride, 2014. "An Experimental Study of Network Formation with Limited Observation," Working Papers 141501, University of California-Irvine, Department of Economics.
    17. Marco Marini, 2007. "An Overview of Coalition & Network Formation Models for Economic Applications," Working Papers 0712, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
    18. De Sinopoli, Francesco & Pimienta, Carlos, 2010. "Costly network formation and regular equilibria," Games and Economic Behavior, Elsevier, vol. 69(2), pages 492-497, July.
    19. Timo Hiller, 2012. "Peer Effects in Endogenous Networks," Bristol Economics Discussion Papers 12/633, Department of Economics, University of Bristol, UK.
    20. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
    21. König, Michael D. & Battiston, Stefano & Napoletano, Mauro & Schweitzer, Frank, 2012. "The efficiency and stability of R&D networks," Games and Economic Behavior, Elsevier, vol. 75(2), pages 694-713.
    22. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    23. Marco A. Marini, 2007. "An Overview of Coalitions and Networks Formation Models for Economic Applications," Working Papers 0707, CREI Università degli Studi Roma Tre, revised 2007.
    24. Berno Buechel & Tim Hellmann, 2012. "Under-connected and over-connected networks: the role of externalities in strategic network formation," Review of Economic Design, Springer;Society for Economic Design, pages 71-87.
    25. Tim Hellmann, 2013. "On the existence and uniqueness of pairwise stable networks," International Journal of Game Theory, Springer;Game Theory Society, pages 211-237.

    More about this item

    Keywords

    Network formation; Pairwise-stability; Proper equilibrium; C62; C72; D85; L14;

    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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