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Equilibrium Selection and Stability for the Groves Ledyard Mechanism

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  • Scott E. Page
  • Troy Tassier

Abstract

In their seminal paper Groves and Ledyard (1976) construct a balanced incentive compatible mechanism that solves the free rider problem. In subsequent research, Bergstrom, Simon, and Titus (1983) prove that there exist numerous asymmetric equilibria in addition to the symmetric equilibrium. In the present paper, we explicitly solve for the additional equilibria and use computational experiments to examine the structure and stability of the set of equilibria of the Groves Ledyard Mechanism. We find that all of the equilibria found by Berstrom, Simon, and Titus are unstable and that for a high level of the punishment parameter these equilibria do not exist. Further, we find that there exists an additional boundary equilibrium for each of the equilibria found by Bergstrom, Simon, and Titus. The boundary equilibria are all stable.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jpbect:v:6:y:2004:i:2:p:311-335
    DOI: 10.1111/j.1467-9779.2004.00168.x
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    File URL: https://doi.org/10.1111/j.1467-9779.2004.00168.x
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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. 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.
    3. 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.
    4. 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.
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    1. 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.
    2. Healy, Paul J. & Jain, Ritesh, 2017. "Generalized Groves–Ledyard mechanisms," Games and Economic Behavior, Elsevier, vol. 101(C), pages 204-217.
    3. , J. & ,, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.

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