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A characterization of equilibria in the Groves-Ledyard mechanism

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  • Page, Scott E.
  • Tassier, Troy

Abstract

In this paper, we characterize all interior and boundary equilibria of the Groves-Ledyard mechanism for a large class of economies and determine their stability properties. We show that the mechanism admits three types of equilibria: a symmetric, efficient, stable interior equilibrium, a large set of asymmetric, efficient, unstable, interior equilibria, and a large set of asymmetric, inefficient, stable boundary equilibria. We further show that asymmetric equilibria fail to exist for large values of the punishment parameter or if the message space is bounded sufficiently. The boundary equilibria previously had not been located nor had the instability of the asymmetric equilibria been known. Interestingly, the stability of the symmetric equilibrium rests on two dynamics that individually produce instability.

Suggested Citation

  • Page, Scott E. & Tassier, Troy, 2010. "A characterization of equilibria in the Groves-Ledyard mechanism," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1229-1242, November.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1229-1242
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    References listed on IDEAS

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    1. 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.
    2. Thomas Muench & Mark Walker, 1983. "Are Groves-Ledyard Equilibria Attainable?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(2), pages 393-396.
    3. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
    4. Van Huyck, John B & Cook, Joseph P & Battalio, Raymond C, 1994. "Selection Dynamics, Asymptotic Stability, and Adaptive Behavior," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 975-1005, October.
    5. Scott E. Page & Troy Tassier, 2004. "Equilibrium Selection and Stability for the Groves Ledyard Mechanism," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(2), pages 311-335, May.
    6. Bergstrom, Theodore & Simon, Carl P. & Titus, Charles J., 1983. "Counting Groves-Ledyard equilibria via degree theory," Journal of Mathematical Economics, Elsevier, vol. 12(2), pages 167-184, October.
    7. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 49-72, January.
    8. 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, vol. 106(3), pages 633-662, June.
    9. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 73-75, January.
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