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Club networks with multiple memberships and noncooperative stability

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  • Page Jr., Frank H.
  • Wooders, Myrna

Abstract

Modeling club structures as bipartite directed networks, we formulate the problem of club formation with multiple memberships as a noncooperative game of network formation and identify conditions on network formation rules and players' network payoffs sufficient to guarantee that the game has a potential function. Our sufficient conditions require that each player choose freely and unilaterally those clubs he joins and also his activities within those clubs (subject to feasibility constraints). We refer to our conditions on rules as noncooperative free mobility. We also require that players' payoffs be additively separable in player-specific payoffs and externalities and that payoff externalities -- a function of club membership, club activities, and crowding -- be identical across players (externality homogeneity). We then show that under these conditions, the noncooperative game of club network formation with multiple memberships is a potential game over directed club networks and we discuss the implications of this result.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 70 (2010)
Issue (Month): 1 (September)
Pages: 12-20

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Handle: RePEc:eee:gamebe:v:70:y:2010:i:1:p:12-20

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Clubs Network formation games Potential games Path dominance core Nash club equilibria Admissible set;

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References

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  12. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  13. Konishi, Hideo & Weber, Shlomo & Le Breton, Michel, 1997. "Free mobility equilibrium in a local public goods economy with congestion," Research in Economics, Elsevier, vol. 51(1), pages 19-30, April.
  14. Hollard, Guillaume, 2000. "On the existence of a pure strategy Nash equilibrium in group formation games," Economics Letters, Elsevier, vol. 66(3), pages 283-287, March.
  15. Allouch, Nizar & Wooders, Myrna, 2008. "Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes," Journal of Economic Theory, Elsevier, vol. 140(1), pages 246-278, May.
  16. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
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Citations

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Cited by:
  1. Jean-François Caulier & Ana Mauleon & Vincent Vannetelbosch, 2013. "Contractually stable networks," International Journal of Game Theory, Springer, vol. 42(2), pages 483-499, May.
  2. Myrna Wooders, 2009. "Market Games and Clubs," Vanderbilt University Department of Economics Working Papers 0919, Vanderbilt University Department of Economics.
  3. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers CIE 74, University of Paderborn, CIE Center for International Economics.
  4. MAULEON, Ana & ROEHL, Nils & VANNETELBOSCH, Vincent, 2014. "Constitutions and social networks," CORE Discussion Papers 2014003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers Dissertations 02, University of Paderborn, Faculty of Business Administration and Economics.
  6. Jean-François Caulier & Ana Mauleon & Jose Sempere-Monerris & Vincent Vannetelbosch, 2013. "Stable and efficient coalitional networks," Review of Economic Design, Springer, vol. 17(4), pages 249-271, December.
  7. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2013. "An allocation rule for dynamic random network formation processes," Documents de travail du Centre d'Economie de la Sorbonne 13063, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  8. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers 74, University of Paderborn, CIE Center for International Economics.

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