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Weak Links, Good Shots and other PublicGood Games: Building on BBV

  • Richard Cornes
  • Roger Hartley

We suggest an alternative way of analyzing the canonical Bergstrom-Blume-Varian model of non-cooperative voluntary contributions to a public good that avoids the proliferation of dimensions as the number of players is increased. We exploit this approach to analyze models in which the aggregate level of public good is determined as a more general social composition function of individual gifts – specifically, as a generalized CES form – rather than as an unweighted sum as well as the weakest-link and best-shot models suggested by Hirshleifer. In each case, we characterize the set of equilibria, in some cases establishing existence of a unique equilibrium as well as briefly pointing out some interesting comparative static properties. We also study the weakest-link and best-shot limits of the CES composition function and show how the former can be used for equilibrium selection and the latter to show that equilibria of some better-shot games are identical to those of the much simpler best-shot game.

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Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 0624.

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Date of creation: 2006
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Handle: RePEc:man:sespap:0624
Contact details of provider: Postal: Manchester M13 9PL
Phone: (0)161 275 4868
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Web page: http://www.socialsciences.manchester.ac.uk/subjects/economics/
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  1. repec:cup:cbooks:9780521834773 is not listed on IDEAS
  2. Okuguchi, Koji, 1993. "Unified approach to Cournot models : Oligopoly, taxation and aggregate provision of a pure public good," European Journal of Political Economy, Elsevier, vol. 9(2), pages 233-245, May.
  3. Ihori, Toshihiro, 1996. "International public goods and contribution productivity differentials," Journal of Public Economics, Elsevier, vol. 61(1), pages 139-154, July.
  4. repec:cup:cbooks:9780521542548 is not listed on IDEAS
  5. Fraser, Clive D., 1992. "The uniqueness of Nash equilibrium in the private provision of public goods : An alternative proof," Journal of Public Economics, Elsevier, vol. 49(3), pages 389-390, December.
  6. Vicary, Simon & Sandler, Todd, 2002. "Weakest-link public goods: Giving in-kind or transferring money," European Economic Review, Elsevier, vol. 46(8), pages 1501-1520, September.
  7. Vicary, Simon, 1990. "Transfers and the weakest-link : An extension of Hirshleifer's analysis," Journal of Public Economics, Elsevier, vol. 43(3), pages 375-394, December.
  8. Richard Cornes & Roger Hartley, 2007. "Aggregative Public Good Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 201-219, 04.
  9. Bergstrom, Ted C. & Blume, Larry & Varian, Hal, 1992. "Uniqueness of Nash equilibrium in private provision of public goods : An improved proof," Journal of Public Economics, Elsevier, vol. 49(3), pages 391-392, December.
  10. Sandler, Todd, 1998. "Global and Regional Public Goods: A Prognosis for Collective Action," Staff General Research Papers 1225, Iowa State University, Department of Economics.
  11. Spence, A Michael, 1980. "Notes on Advertising, Economies of Scale, and Entry Barriers," The Quarterly Journal of Economics, MIT Press, vol. 95(3), pages 493-507, November.
  12. Cornes, Richard, 1993. "Dyke Maintenance and Other Stories: Some Neglected Types of Public Goods," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 259-71, February.
  13. Sandler, Todd & Vicary, Simon, 2001. "Weakest-link public goods: giving in-kind or transferring money in a sequential game," Economics Letters, Elsevier, vol. 74(1), pages 71-75, December.
  14. Jack Hirshleifer, 1983. "From weakest-link to best-shot: The voluntary provision of public goods," Public Choice, Springer, vol. 41(3), pages 371-386, 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. Roberto A. Weber, 2006. "Managing Growth to Achieve Efficient Coordination in Large Groups," American Economic Review, American Economic Association, vol. 96(1), pages 114-126, March.
  17. Arce M., Daniel G. & Sandler, Todd, 2001. "Transnational public goods: strategies and institutions," European Journal of Political Economy, Elsevier, vol. 17(3), pages 493-516, September.
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