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

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  • Richard Cornes
  • Roger Hartley

Abstract

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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Bibliographic Info

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

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References

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  1. 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.
  2. Sandler,Todd, 2004. "Global Collective Action," Cambridge Books, Cambridge University Press, number 9780521834773.
  3. 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.
  4. 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.
  5. 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.
  6. Richard Cornes & Roger Hartley, 2003. "Aggregative Public Goods Games," NajEcon Working Paper Reviews 666156000000000063, www.najecon.org.
  7. 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.
  8. Todd Sandler, 1998. "Global and regional public goods: a prognosis for collective action," Fiscal Studies, Institute for Fiscal Studies, vol. 19(3), pages 221-247, August.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
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Citations

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Cited by:
  1. Acocella Nicola & Di Bartolomeo Giovanni, 2010. "Conflict of interest and coordination in public good provision," Politica economica, Società editrice il Mulino, issue 3, pages 389-408.
  2. Kolmar, Martin & Rommeswinkel, Hendrik, 2013. "Contests with group-specific public goods and complementarities in efforts," Journal of Economic Behavior & Organization, Elsevier, vol. 89(C), pages 9-22.
  3. Maoliang Ye & Sam Asher & Lorenzo Casaburi & Plamen Nikolov, 2010. "One step at a time: Does gradualism build coordination?," Framed Field Experiments 00188, The Field Experiments Website.
  4. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
  5. Subhasish M. Chowdhury & Dongryul Lee & Iryna Topolyan, 2013. "The Max-Min Group Contest," University of East Anglia Applied and Financial Economics Working Paper Series 050, School of Economics, University of East Anglia, Norwich, UK..
  6. Martin Gregor, 2013. "Modeling positive inter-jurisdictional public spending spillovers," EcoMod2013 5193, EcoMod.
  7. Martin Gregor & Lenka Šastná, 2011. "The Decentralization Tradeoff for Complementary Spillovers," Working Papers IES 2011/13, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Apr 2011.
  8. Lee, Dongryul, 2012. "Weakest-link contests with group-specific public good prizes," European Journal of Political Economy, Elsevier, vol. 28(2), pages 238-248.
  9. Ghislain Dutheil de la Rochère & Jean-Michel Josselin & Yvon Rocaboy, 2011. "The role of aggregation technologies in the provision of supranational public goods: A reconsideration of NATO’s strategies," The Review of International Organizations, Springer, vol. 6(1), pages 85-103, March.
  10. Kirchgässner, Gebhard, 2010. "On minimal morals," European Journal of Political Economy, Elsevier, vol. 26(3), pages 330-339, September.
  11. Stefano Barbieri & David Malueg, 2014. "Group efforts when performance is determined by the “best shot”," Economic Theory, Springer, vol. 56(2), pages 333-373, June.
  12. Martin Gregor, 2011. "Tradeoffs of foreign assistance for the weakest-link global public goods," International Tax and Public Finance, Springer, vol. 18(2), pages 233-251, April.

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