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Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes

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  • Allouch, Nizar
  • Wooders, Myrna

Abstract

We model an economy with clubs (or jurisdictions) where individuals may belong to multiple clubs and where clubs sizes are arbitrary--clubs may be restricted to consist of only one or two persons, or as large as the entire economy, or anything in-between. Notions of price-taking equilibrium and the core, both with communication costs, are introduced. These notions take into account that there is a small communication cost of deviating from a given outcome. We demonstrate that, given communication costs, for all sufficiently large economies the core is nonempty and the set of price-taking equilibrium outcomes is equivalent to the core.

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  • 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.
  • Handle: RePEc:eee:jetheo:v:140:y:2008:i:1:p:246-278
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    Cited by:

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    2. Nizar Allouch, 2010. "A Core‐Equilibrium Convergence in a Public Goods Economy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(4), pages 857-870, August.
    3. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2019. "Paths to stability for overlapping group structures," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 19-24.
    4. Hideo Konishi & Ryusuke Shinohara, 2014. "Voluntary Participation and Provision of Public Goods in Large Finite Economies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(2), pages 173-195, April.
    5. Yusuke Kamishiro & Roberto Serrano & Myrna Wooders, 2021. "Monopolists of scarce information and small group effectiveness in large quasilinear economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 801-827, December.
    6. Gersbach, Hans & Haller, Hans, 2010. "Club theory and household formation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 715-724, September.
    7. Myrna Wooders, 2010. "Cores of many-player games; nonemptiness and equal treatment," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 131-162, March.
    8. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
    9. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    10. Nizar Allouch & Myrna Wooders, 2017. "On the nonemptiness of approximate cores of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 191-209, January.
    11. van den Nouweland, Anne & Wooders, Myrna, 2011. "Share equilibrium in local public good economies," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 376-381.
    12. van den Nouweland, A. & Wooders, M., 2017. "Existence of share equilibrium in symmetric local public good economies," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 50-60.
    13. 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.
    14. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2018. "Constitutions and groups," Games and Economic Behavior, Elsevier, vol. 107(C), pages 135-152.
    15. Anne Van den nouweland & Myrna Wooders, 2016. "Existence of Share Equilibrium in Symmetric Local Public Good Economies∗," Vanderbilt University Department of Economics Working Papers 16-00008, Vanderbilt University Department of Economics.
    16. 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.
    17. Marta Faias & Jaime Luque, 2017. "Endogenous formation of security exchanges," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 331-355, August.
    18. Manjunath, Vikram, 2016. "Fractional matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 321-336.
    19. Rabah Amir & Jean Gabszewicz & Joana Resende, 2014. "Thematic Clubs and the Supremacy of Network Externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(5), pages 706-729, October.
    20. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
    21. Faias, Marta & Moreno-García, Emma, 2022. "On the use of public goods," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 58-63.

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