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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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  • Page Jr., Frank H. & Wooders, Myrna, 2010. "Club networks with multiple memberships and noncooperative stability," Games and Economic Behavior, Elsevier, vol. 70(1), pages 12-20, September.
    • Handle: RePEc:eee:gamebe:v:70:y:2010:i:1:p:12-20
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    4. Jean-François Caulier & Ana Mauleon & Jose Sempere-Monerris & Vincent Vannetelbosch, 2013. "Stable and efficient coalitional networks," Review of Economic Design, Springer;Society for Economic Design, vol. 17(4), pages 249-271, December.
    5. Mitri Kitti & Matti Pihlava & Hannu Salonen, 2016. "Search in Networks: The Case of Board Interlocks," Discussion Papers 116, Aboa Centre for Economics.
    6. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    7. Jung, Hohyun, 2023. "Eliminating the biases of user influence and item popularity in bipartite networks: A case study of Flickr and Netflix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    8. 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.
    9. Hitomu Kotani & Muneta Yokomatsu, 2019. "Quantitative evaluation of the roles of community events and artifacts for social network formation: a multilayer network model of a community of practice," Computational and Mathematical Organization Theory, Springer, vol. 25(4), pages 428-463, December.
    10. Gong, Rui & He, Jieshuang & Page, Frank, 2016. "Incentive compatible networks and the delegated networking principle," LSE Research Online Documents on Economics 66045, London School of Economics and Political Science, LSE Library.
    11. Sihua Ding & Marcin Dziubiński & Sanjeev Goyal, 2021. "Clubs and Networks," Working Papers 20210073, New York University Abu Dhabi, Department of Social Science, revised Dec 2021.
    12. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2018. "Constitutions and groups," Games and Economic Behavior, Elsevier, vol. 107(C), pages 135-152.
    13. Ngoc M. Nguyen & Lionel Richefort & Thomas Vallée, 2020. "Endogenous formation of multiple social groups," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(5), pages 1368-1390, September.
    14. Fu, Jing & Page, Frank & Zigrand, Jean-Pierre, 2022. "Layered networks, equilibrium dynamics, and stable coalitions," LSE Research Online Documents on Economics 118874, London School of Economics and Political Science, LSE Library.
    15. Gong, Rui & Page, Frank & Wooders, Myrna, 2015. "Endogenous correlated network dynamics," LSE Research Online Documents on Economics 65098, London School of Economics and Political Science, LSE Library.
    16. Sokolov, Denis, 2022. "Shapley value for TU-games with multiple memberships and externalities," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 76-90.
    17. Jing Fu & Frank Page & Jean-Pierre Zigrand, 2023. "Correction to: Layered Networks, Equilibrium Dynamics, and Stable Coalitions," Dynamic Games and Applications, Springer, vol. 13(2), pages 669-704, June.
    18. Jing Fu & Frank Page & Jean-Pierre Zigrand, 2023. "Layered Networks, Equilibrium Dynamics, and Stable Coalitions," Dynamic Games and Applications, Springer, vol. 13(2), pages 636-668, June.

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