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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 140 (2008)
Issue (Month): 1 (May)
Pages: 246-278

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Handle: RePEc:eee:jetheo:v:140:y:2008:i:1:p:246-278

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. Le Breton, Michel & Weber, Shlomo, 2003. "The Art of Making Everybody Happy : How to Prevent a Secession," IDEI Working Papers 164, Institut d'Économie Industrielle (IDEI), Toulouse.
  2. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William Zame, 1997. "Clubs and the Market: Large Finite Economies," UCLA Economics Working Papers 766, UCLA Department of Economics.
  3. Foley, Duncan K, 1970. "Lindahl's Solution and the Core of an Economy with Public Goods," Econometrica, Econometric Society, vol. 38(1), pages 66-72, January.
  4. Kovalenkov, Alexander & Wooders, Myrna, 2004. "Comparative Statics And Laws Of Scarcity For Games," The Warwick Economics Research Paper Series (TWERPS) 715, University of Warwick, Department of Economics.
  5. Harold L Cole & Edward C Prescott, 1997. "Valuation equilibrium with Clubs," Levine's Working Paper Archive 912, David K. Levine.
  6. HILDENBRAND, Werner & KIRMAN, Alan P., . "Size removes inequity," CORE Discussion Papers RP -143, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Michel Le Breton & Shlomo Weber, 2003. "The Art of Making Everybody Happy: How to Prevent a Secession," IMF Staff Papers, Palgrave Macmillan, vol. 50(3), pages 4.
  8. Alexander Kovalenkov & Myrna H. Wooders, 1998. "Approximate cores of games and economies with clubs," Working Papers mwooders-00-01, University of Toronto, Department of Economics.
  9. Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies," Journal of Economic Theory, Elsevier, vol. 49(1), pages 135-168, October.
  10. Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw, 1985. "Edgeworth Equilibria," Cowles Foundation Discussion Papers 756R, Cowles Foundation for Research in Economics, Yale University.
    • Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-37, September.
  11. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-85, September.
  12. Boyd, John H, III & McKenzie, Lionel W, 1993. "The Existence of Competitive Equilibrium over an Infinite Horizon with Production and General Consumption Sets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 1-20, February.
  13. Wooders, Myrna Holtz, 1988. "Stability of jurisdiction structures in economies with local public goods," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 29-49, February.
  14. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  15. Myrna Wooders & Alexander Kovalenkov, 2001. "Epsilon cores of games with limited side payments Nonemptiness and equal treatment," Economics Bulletin, AccessEcon, vol. 28(5), pages A0.
  16. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2005. "Transfers in a polarized country: bridging the gap between efficiency and stability," Journal of Public Economics, Elsevier, vol. 89(7), pages 1277-1303, July.
  17. Hammond, Peter J. & Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "Continuum economies with finite coalitions: Core, equilibria, and widespread externalities," Journal of Economic Theory, Elsevier, vol. 49(1), pages 113-134, October.
  18. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  19. Wooders, Myrna, 1978. "Equilibria, the core, and jurisdiction structures in economies with a local public good," Journal of Economic Theory, Elsevier, vol. 18(2), pages 328-348, August.
  20. Alexander Kovalenkov & Myrna H. Wooders, 1999. "An explicit bound on epsilon for nonemptiness of Epsilon-cores of games," Working Papers mwooders-00-03, University of Toronto, Department of Economics.
  21. Mas-Colell, Andreu, 1977. "Indivisible commodities and general equilibrium theory," Journal of Economic Theory, Elsevier, vol. 16(2), pages 443-456, December.
  22. Gilles, Robert P. & Scotchmer, Suzanne, 1997. "Decentralization in Replicated Club Economies with Multiple Private Goods," Journal of Economic Theory, Elsevier, vol. 72(2), pages 363-387, February.
  23. Edgeworth, Francis Ysidro, 1881. "Mathematical Psychics," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number edgeworth1881.
  24. Kovalenkov, Alexander & Wooders, Myrna, 2003. "Laws of Scarcity for a Finite Game : Exact Bounds on Estimations," The Warwick Economics Research Paper Series (TWERPS) 691, University of Warwick, Department of Economics.
  25. Wooders, Myrna Holtz, 1992. "Inessentiality of Large Groups and the Approximate Core Property: An Equivalence Theorem," Economic Theory, Springer, vol. 2(1), pages 129-47, January.
  26. Aliprantis, Charalambos D. & Brown, Donald J. & Burkinshaw, Owen, 1987. "Edgeworth equilibria in production economies," Journal of Economic Theory, Elsevier, vol. 43(2), pages 252-291, December.
  27. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1998. "Equilibrium in a Finite Local Public Goods Economy," Journal of Economic Theory, Elsevier, vol. 79(2), pages 224-244, April.
  28. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  29. Conley, John P. & Wooders, Myrna H., 1997. "Equivalence of the Core and Competitive Equilibrium in a Tiebout Economy with Crowding Types," Journal of Urban Economics, Elsevier, vol. 41(3), pages 421-440, May.
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Citations

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Cited by:
  1. repec:pdn:wpaper:74 is not listed on IDEAS
  2. repec:pdn:dispap:02 is not listed on IDEAS
  3. Frank H. Page, Jr., Myrna H. Wooders, 2009. "Club Networks with Multiple Memberships and Noncooperative Stability," Caepr Working Papers 2009-005, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  4. Myrna Wooders, 2010. "Cores of many-player games; nonemptiness and equal treatment," Review of Economic Design, Springer, vol. 14(1), pages 131-162, March.
  5. Hans Gersbach & Hans Haller, 2009. "Club Theory and Household Formation," CER-ETH Economics working paper series 09/110, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  6. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
  7. 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.
  8. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers CIE 74, University of Paderborn, CIE Center for International Economics.
  9. 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.
  10. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
  11. Hideo Konishi & Ryusuke Shinohara, 2011. "Voluntary Participation and the Provision of Public Goods in Large Finite Economies," Boston College Working Papers in Economics 776, Boston College Department of Economics.

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