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Contributing or Free-Riding? Voluntary Participation in a Public Good Economy

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  • Taiji Furusawa
  • Hideo Konishi

Abstract

We consider a (pure) public goods provision problem with voluntary participation in a quasi-linear economy. We propose a new hybrid solution concept, the free-riding-proof core (FRP-Core), which endogenously determines a contribution group, public good provision level, and its cost-sharing. The FRP-Core is always nonempty in public good economies but does not usually achieve global efficiency. The FRP-Core has support from both cooperative and noncooperative games. In particular, it is equivalent to the set of perfectly coalition-proof Nash equilibrium (Bernheim, Peleg, and Whinston, 1987) of a dynamic game with players' participation decisions followed by a common agency game of public goods provision. We illustrate various properties of the FRPCore with an example. We also show that the equilibrium level of public good shrinks to zero as the economy is replicated.

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Bibliographic Info

Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd09-128.

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Date of creation: Mar 2010
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Handle: RePEc:hst:ghsdps:gd09-128

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Keywords: endogenous coalition formation; externalities; public good; perfectly coalition-proof Nash equilibrium; free-riders; free-riding-proof core; lobbying; common agency game;

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References

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  1. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 217-25, April.
  2. Laussel, Didier & Le Breton, Michel, 1998. "Efficient Private Production of Public Goods under Common Agency," Games and Economic Behavior, Elsevier, vol. 25(2), pages 194-218, November.
  3. Laussel, Didier & Le Breton, Michel, 2001. "Conflict and Cooperation: The Structure of Equilibrium Payoffs in Common Agency," Journal of Economic Theory, Elsevier, vol. 100(1), pages 93-128, September.
  4. Le Breton, Michel & Salanie, Francois, 2003. "Lobbying under political uncertainty," Journal of Public Economics, Elsevier, vol. 87(12), pages 2589-2610, December.
  5. Paul Healy, 2010. "Equilibrium participation in public goods allocations," Review of Economic Design, Springer, vol. 14(1), pages 27-50, March.
  6. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1999. "On Coalition-Proof Nash Equilibria in Common Agency Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 122-139, March.
  7. Palfrey, Thomas R. & Rosenthal, Howard, 1984. "Participation and the provision of discrete public goods: a strategic analysis," Journal of Public Economics, Elsevier, vol. 24(2), pages 171-193, July.
  8. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
  9. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954, September.
  10. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
  11. Maruta, Toshimasa & Okada, Akira, 2005. "Group Formation and Heterogeneity in Collective Action Games," Discussion Papers 2005-07, Graduate School of Economics, Hitotsubashi University.
  12. Milleron, Jean-Claude, 1972. "Theory of value with public goods: A survey article," Journal of Economic Theory, Elsevier, vol. 5(3), pages 419-477, December.
  13. Debraj Ray & Rajiv Vohra, 2001. "Coalitional Power and Public Goods," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1355-1384, December.
  14. Devashish Mitra, 1999. "Endogenous Lobby Formation and Endogenous Protection: A Long-Run Model of Trade Policy Determination," American Economic Review, American Economic Association, vol. 89(5), pages 1116-1134, December.
  15. Bombardini, Matilde, 2008. "Firm heterogeneity and lobby participation," Journal of International Economics, Elsevier, vol. 75(2), pages 329-348, July.
  16. 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.
  17. Saijo, Tatsuyoshi & Yamato, Takehiko, 1999. "A Voluntary Participation Game with a Non-excludable Public Good," Journal of Economic Theory, Elsevier, vol. 84(2), pages 227-242, February.
  18. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
  19. Conley John P., 1994. "Convergence Theorems on the Core of a Public Goods Economy: Sufficient Conditions," Journal of Economic Theory, Elsevier, vol. 62(1), pages 161-185, February.
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Citations

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Cited by:
  1. 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.
  2. Zudenkova, Galina, 2010. "Sincere Lobby Formation," Working Papers 2072/151545, Universitat Rovira i Virgili, Department of Economics.
  3. Federico Quartieri, 2013. "Coalition-proofness under weak and strong Pareto dominance," Social Choice and Welfare, Springer, vol. 40(2), pages 553-579, February.
  4. Noriaki Matsushima & Ryusuke Shinohara, 2012. "Private Provision of Public Goods that are Complements for Private Goods: Application to Open Source Software Developments," ISER Discussion Paper 0830, Institute of Social and Economic Research, Osaka University.
  5. Ryusuke Shinohara, 2010. "Coalition-proof equilibria in a voluntary participation game," International Journal of Game Theory, Springer, vol. 39(4), pages 603-615, October.
  6. FURUSAWA Taiji & KONISHI Hideo, 2011. "Free-Riding-Proof International Environmental Agreements," Discussion papers 11043, Research Institute of Economy, Trade and Industry (RIETI).
  7. Yukihiro Nishimura & Ryusuke Shinohara, 2013. "A voluntary participation game through a unit-by-unit cost share mechanism of a non-excludable public good," Social Choice and Welfare, Springer, vol. 40(3), pages 793-814, March.
  8. Zudenkova, Galina, 2012. "Lobbying as a Guard against Extremism," Working Papers 2072/184036, Universitat Rovira i Virgili, Department of Economics.

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