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A Simple Supermodular Mechanism that Implements Lindahl Allocations

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  • Van Essen, Matthew J.

Abstract

This paper introduces a new incentive compatible mechanism which for general preference environments implements Lindahl allocations as Nash equilibria. The mechanism does not increase in structural complexity as consumers are added to the economy, the minimum dimension of data needed to compute payoffs is smaller than other mechanisms with comparable properties; and for quasi-linear environments, the mechanism induces a supermodular game for appropriate choices of the mechanism parameters. Thus, this new Lindahl mechanism provides a connection between the desirable welfare properties of Lindahl allocations and the desirable theoretical/ convergence properties of supermodular games.

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File URL: http://mpra.ub.uni-muenchen.de/12781/
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File URL: http://mpra.ub.uni-muenchen.de/15277/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12781.

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Date of creation: 15 Jan 2008
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Handle: RePEc:pra:mprapa:12781

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Keywords: Lindahl Equilibrium; Nash Implementation; Supermodular Games;

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References

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  1. Muench, Thomas & Walker, Mark, 1983. "Are Groves-Ledyard Equilibria Attainable? [Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem]," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 50(2), pages 393-96, April.
  2. Milleron, Jean-Claude, 1972. "Theory of value with public goods: A survey article," Journal of Economic Theory, Elsevier, Elsevier, vol. 5(3), pages 419-477, December.
  3. Yan Chen & Robert S. Gazzale, 2004. "When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting," Department of Economics Working Papers, Department of Economics, Williams College 2004-02, Department of Economics, Williams College.
  4. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 46(2), pages 217-25, April.
  5. Walker, Mark, 1980. "On the Nonexistence of a Dominant Strategy Mechanism for Making Optimal Public Decisions," Econometrica, Econometric Society, Econometric Society, vol. 48(6), pages 1521-40, September.
  6. Foley, Duncan K, 1970. "Lindahl's Solution and the Core of an Economy with Public Goods," Econometrica, Econometric Society, Econometric Society, vol. 38(1), pages 66-72, January.
  7. Smith, Vernon L, 1979. " An Experimental Comparison of Three Public Good Decision Mechanisms," Scandinavian Journal of Economics, Wiley Blackwell, Wiley Blackwell, vol. 81(2), pages 198-215.
  8. AMIR, Rabah, 2003. "Supermodularity and complementarity in economics: an elementary survey," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2003104, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Bailey, Martin J, 1994. " Lindahl Mechanisms and Free Riders," Public Choice, Springer, Springer, vol. 80(1-2), pages 35-39, July.
  10. Bergstrom, Theodore C & Cornes, Richard C, 1983. "Independence of Allocative Efficiency from Distribution in the Theory of Public Goods," Econometrica, Econometric Society, Econometric Society, vol. 51(6), pages 1753-65, November.
  11. Smith, Vernon L, 1980. "Experiments with a Decentralized Mechanism for Public Good Decisions," American Economic Review, American Economic Association, American Economic Association, vol. 70(4), pages 584-99, September.
  12. Yan Chen & Fang-Fang Tang, 1998. "Learning and Incentive-Compatible Mechanisms for Public Goods Provision: An Experimental Study," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 106(3), pages 633-662, June.
  13. Kim, Taesung, 1993. "A stable Nash mechanism implementing Lindahl allocations for quasi-linear environments," Journal of Mathematical Economics, Elsevier, vol. 22(4), pages 359-371.
  14. Vega-Redondo, Fernando, 1989. "Implementation of Lindahl equilibrium: an integration of the static and dynamic approaches," Mathematical Social Sciences, Elsevier, Elsevier, vol. 18(3), pages 211-228, December.
  15. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, Econometric Society, vol. 49(1), pages 65-71, January.
  16. Groves, Theodore & Ledyard, John O, 1980. "The Existence of Efficient and Incentive Compatible Equilibria with Public Goods," Econometrica, Econometric Society, Econometric Society, vol. 48(6), pages 1487-1506, September.
  17. Healy, Paul J., 2006. "Learning dynamics for mechanism design: An experimental comparison of public goods mechanisms," Journal of Economic Theory, Elsevier, Elsevier, vol. 129(1), pages 114-149, July.
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Citations

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Cited by:
  1. Matt Van Essen, 2012. "A note on the stability of Chen’s Lindahl mechanism," Social Choice and Welfare, Springer, Springer, vol. 38(2), pages 365-370, February.
  2. Healy, Paul J. & Mathevet, Laurent, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, Econometric Society, vol. 7(3), September.
  3. Matt Van Essen, 2012. "Information complexity, punishment, and stability in two Nash efficient Lindahl mechanisms," Review of Economic Design, Springer, Springer, vol. 16(1), pages 15-40, March.

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