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

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Abstract

This paper develops a model of an economy with clubs where individuals may belong to multiple clubs and where there may be ever increasing returns to club size. Clubs may be large, as large as the total agent set. The main condition required is that sufficient wealth can compensate for memberships in larger and larger clubs. Notions of price taking equilibrium and the core, both with communication costs, are introduced. These notions require that there is a small cost, called a communication cost, of deviating from a given outcome. With some additional standard sorts of assumptions on preferences, we demonstrate that for all sufficiently large economies, the core is non-empty and contains states of the economy that are in the core of the replicated economy for all replications (Edgeworth states of the economy). Moreover, for any given economy, every state of the economy that is in the core for all replications of that economy can be supported as a price-taking equilibrium with communication costs. Together these two results imply that, given the communication costs, for all sufficiently large economies there exists Edgeworth states of the economy and every Edgeworth state can be supported as a price-taking equilibrium.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04109.pdf
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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b04109.

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Length: 32 pages
Date of creation: Feb 2004
Date of revision:
Handle: RePEc:mse:wpsorb:b04109

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Keywords: Congestion; clubs; equilibrium.;

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References

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  1. Alexander Kovalenkov & Myrna Holtz Wooders, 2000. "Approximate Cores of Games and Economies with Clubs," Econometric Society World Congress 2000 Contributed Papers 1790, Econometric Society.
  2. Myrna Holtz Wooders, 1996. "Equivalence of Lindahl equilibrium with participation prices and the core (*)," Economic Theory, Springer, vol. 9(1), pages 115-127.
  3. D. K. Foley, 1967. "Lindahl's Solution and the Core of an Economy with Public Goods," Working papers 3, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Harold L Cole & Edward C Prescott, 1997. "Valuation equilibrium with Clubs," Levine's Working Paper Archive 912, David K. Levine.
  5. Bryan Ellickson and Birgit Grodal, Suzanne Scotchmer, and William R.Zame., 1997. "Clubs and the Market: Large Finite Economies," Economics Working Papers 97-255, University of California at Berkeley.
  6. Kovalenkov, Alexander & Wooders, Myrna Holtz, 2001. "Epsilon Cores of Games with Limited Side Payments: Nonemptiness and Equal Treatment," Games and Economic Behavior, Elsevier, vol. 36(2), pages 193-218, August.
  7. 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.
  8. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R Zame, 2003. "Clubs and the Market," Levine's Working Paper Archive 618897000000000754, David K. Levine.
    • Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, September.
  9. 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.
  10. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  11. Bewley, Truman F, 1981. "A Critique of Tiebout's Theory of Local Public Expenditures," Econometrica, Econometric Society, vol. 49(3), pages 713-40, May.
  12. Broome, John, 1972. "Approximate equilibrium in economies with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 5(2), pages 224-249, October.
  13. 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.
  14. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-85, September.
  15. 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.
  16. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  17. 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.
  18. 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.
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Cited by:
  1. Nizar Allouch & John P. Conley & Myrna Wooders, 2008. "Anonymous Price Taking Equilibrium in Tiebout Economies with a Continuum of Agents: Existence and Characterization," Vanderbilt University Department of Economics Working Papers 0811, Vanderbilt University Department of Economics.
  2. Nizar Allouch & John P. Conley & Myrna Wooders, 2006. "Anonymous Price Taking Equilibrium in Tiebout Economies with Unbounded Club Sizes," Working Papers 556, Queen Mary, University of London, School of Economics and Finance.

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