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A Strategic market game approach for the private provision of public goods

  • Faias, Marta
  • Moreno, Emma
  • Wooders, Myrna

Bergstrom, Blume and Varian (1986) provides an elegant game-theoretic model of an economy with one private good and one public good. Strategies of players consist of voluntary contributions of the private good to public good production. Without relying on first order conditions, the authors demonstrate existence of Nash equilibrium and an extension of Warr's neutrality result -- any redistribution of endowment that left the set of contributors unchanged would induce a new equilibrium with the same total public good provision. The assumption of one-private good greatly facilities the results. We provide analogues of the Bergstrom, Blume and Varian results in a model allowing multiple private and public goods. In addition, we relate the strategic market game equilibrium to the private provision of equilibrium of Villanaci and Zenginobuz (2005), which provides a counter-part to the Walrasian equilibrium for a public goods economy. Our techniques follow those of Dubey and Geanakoplos (2003), which itself grows out of the seminal work of Shapley and Shubik (1977). Our approach also incorporates, into the strategic market game literature, economies with production, not previously treated and, as a by-product, establishes a new existence of private-provision equilibrium.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 37777.

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Date of creation: Dec 2009
Date of revision: 08 Mar 2012
Handle: RePEc:pra:mprapa:37777
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  1. Rabah Amir & Siddhartha Sahi & Martin Shubik, 1986. "A Strategic Market Game with Complete Markets," Cowles Foundation Discussion Papers 814R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  2. 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.
  3. Villanacci, Antonio & Zenginobuz, Unal, 2001. "On the neutrality of redistribution in a general equilibrium model with public goods," MPRA Paper 190, University Library of Munich, Germany, revised 09 Aug 2005.
  4. Kemp, Murray C., 1984. "A note of the theory of international transfers," Economics Letters, Elsevier, vol. 14(2-3), pages 259-262.
  5. Peck, James & Shell, Karl & Spear, Stephen E., 1992. "The market game: existence and structure of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 271-299.
  6. Itaya, Jun-ichi & de Meza, David & Myles, Gareth D, 2002. " Income Distribution, Taxation, and the Private Provision of Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(3), pages 273-97.
  7. Dubey, Pradeep & Geanakoplos, John, 2003. "From Nash to Walras via Shapley-Shubik," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 391-400, July.
  8. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
  9. Villanacci, Antonio & Zenginobuz, Ünal, 2012. "Subscription equilibrium with production: Non-neutrality and constrained suboptimality," Journal of Economic Theory, Elsevier, vol. 147(2), pages 407-425.
  10. Martin Shubik & Jingang Zhao, 1990. "A Strategic Market Game of a Finite Economy with a Mutual Bank," Cowles Foundation Discussion Papers 961, Cowles Foundation for Research in Economics, Yale University.
  11. Richard Cornes & Jun-Ichi Itaya, 2010. "On the Private Provision of Two or More Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(2), pages 363-385, 04.
  12. Monique Florenzano, 2009. "Walras-Lindahl-Wicksell: What equilibrium concept for public goods provision," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00531434, HAL.
  13. Koutsougeras, Leonidas C., 2003. "Convergence to no arbitrage equilibria in market games," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 401-420, July.
  14. Koutsougeras, Leonidas C., 2003. "Non-Walrasian equilibria and the law of one price," Journal of Economic Theory, Elsevier, vol. 108(1), pages 169-175, January.
  15. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
  16. Villanacci, Antonio & Zenginobuz, E.Unal, 2005. "Existence and regularity of equilibria in a general equilibrium model with private provision of a public good," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 617-636, August.
  17. Nizar Allouch, 2012. "On the Private Provision of Public Goods on Networks," Working Papers 689, Queen Mary University of London, School of Economics and Finance.
  18. Muench, Thomas J., 1972. "The core and the Lindahl equilibrium of an economy with a public good: an example," Journal of Economic Theory, Elsevier, vol. 4(2), pages 241-255, April.
  19. Andreoni, James, 1988. "Privately provided public goods in a large economy: The limits of altruism," Journal of Public Economics, Elsevier, vol. 35(1), pages 57-73, February.
  20. Amir, Rabah & Bloch, Francis, 2009. "Comparative statics in a simple class of strategic market games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 7-24, January.
  21. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-68, October.
  22. Warr, Peter G., 1983. "The private provision of a public good is independent of the distribution of income," Economics Letters, Elsevier, vol. 13(2-3), pages 207-211.
  23. Joaquim Silvestre, 2012. "All but one free ride when wealth effects are small," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 201-207, March.
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