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Club Networks with Multiple Memberships and Noncooperative Stability

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

    (Indiana University Bloomington Vanderbilt University)

Abstract

Modeling club structures as bipartite directed networks, we formulate the problem of club formation 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 on network formation rules require that each player be choose freely and unilaterally those clubs he joins and also his activities within these clubs (subject to his set of feasible actions). 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 (additive separability) 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 is a potential game over directed club networks and we discuss the implications of this result.

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File URL: http://www.iub.edu/~caepr/RePEc/PDF/2009/CAEPR2009-005.pdf
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Bibliographic Info

Paper provided by Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington in its series Caepr Working Papers with number 2009-005.

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Length: 16 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:inu:caeprp:2009-005

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  1. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
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  3. 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.
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  6. 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.
  7. 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.
  8. Demange, G., 1991. "Intermediate Preferences and Stable Coalition Structures," DELTA Working Papers 91-16, DELTA (Ecole normale supérieure).
  9. 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.
  10. 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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  13. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
  14. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  15. Kalai, Ehud & Pazner, Elisha A & Schmeidler, David, 1976. "Collective Choice Correspondences as Admissible Outcomes of Social Bargaining Processes," Econometrica, Econometric Society, vol. 44(2), pages 233-40, March.
  16. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  17. Slikker, Marco & Dutta, Bhaskar & van den Nouweland, Anne & Tijs, Stef, 2000. "Potential maximizers and network formation," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 55-70, January.
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Citations

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Cited by:
  1. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers Dissertations 02, University of Paderborn, Faculty of Business Administration and Economics.
  2. repec:hal:cesptp:hal-00633611 is not listed on IDEAS
  3. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
  4. CAULIER, Jean-François & MAULEON, Ana & VANNETELBOSCH, Vincent, 2008. "Contractually stable networks," CORE Discussion Papers 2008066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. CAULIER, Jean-François & MAULEON, Ana & SEMPERE-MONERRIS, José J. & VANNETELBOSCH, Vincent, 2011. "Stable and efficient coalitional networks," CORE Discussion Papers 2011039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. 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).
  7. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers CIE 74, University of Paderborn, CIE Center for International Economics.
  8. 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.
  9. repec:pdn:wpaper:74 is not listed on IDEAS

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