IDEAS home Printed from https://ideas.repec.org/a/the/publsh/898.html
   My bibliography  Save this article

Designing stable mechanisms for economic environments

Author

Listed:
  • Healy, Paul J.

    () (Department of Economics, Ohio State University)

  • Mathevet, Laurent

    () (Department of Economics, University of Texas)

Abstract

We study the design of mechanisms that implement Lindahl or Walrasian allocations and whose Nash equilibria are dynamically stable for a wide class of adaptive dynamics. We argue that supermodularity is not a desirable stability criterion in this mechanism design context, focusing instead on contractive mechanisms. We provide necessary and sufficient conditions for a mechanism to Nash implement Lindahl or Walrasian allocations, show that these conditions are inconsistent with the contraction property when message spaces are one-dimensional, and then show how to use additional dimensions to achieve dynamic stability while gaining budget balance out of equilibrium.

Suggested Citation

  • Healy, Paul J. & Mathevet, Laurent, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
  • Handle: RePEc:the:publsh:898
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20120609/7379/238
    Download Restriction: no

    References listed on IDEAS

    as
    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. 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.
    3. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters,in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404 World Scientific Publishing Co. Pte. Ltd..
    4. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
    5. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
    6. Harstad, Ronald M. & Marrese, Michael, 1982. "Behavioral explanations of efficient public good allocations," Journal of Public Economics, Elsevier, vol. 19(3), pages 367-383, December.
    7. Van Essen, Matthew & Lazzati, Natalia & Walker, Mark, 2012. "Out-of-equilibrium performance of three Lindahl mechanisms: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 74(1), pages 366-381.
    8. Chen, Yan, 2008. "Incentive-compatible Mechanisms for Pure Public Goods: A Survey of Experimental Research," Handbook of Experimental Economics Results, Elsevier.
    9. William H. Sandholm, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 667-689.
    10. Matt Van Essen, 2012. "A note on the stability of Chen’s Lindahl mechanism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 365-370, February.
    11. Yan Chen & Robert Gazzale, 2004. "When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting," American Economic Review, American Economic Association, vol. 94(5), pages 1505-1535, December.
    12. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-438, March.
    13. Mount, Kenneth & Reiter, Stanley, 1974. "The informational size of message spaces," Journal of Economic Theory, Elsevier, vol. 8(2), pages 161-192, June.
    14. Hurwicz,Leonid & Reiter,Stanley, 2008. "Designing Economic Mechanisms," Cambridge Books, Cambridge University Press, number 9780521724104, April.
    15. Walker, Mark, 1984. "A simple auctioneerless mechanism with Walrasian properties," Journal of Economic Theory, Elsevier, vol. 32(1), pages 111-127, February.
    16. Sefton, Martin & Yavas, Abdullah, 1996. "Abreu-Matsushima Mechanisms: Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 16(2), pages 280-302, October.
    17. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
    18. Reiter, Stanley, 1974. "Informational efficiency of iterative processes and the size of message spaces," Journal of Economic Theory, Elsevier, vol. 8(2), pages 193-205, June.
    19. Groves, Theodore & Ledyard, John O, 1980. "The Existence of Efficient and Incentive Compatible Equilibria with Public Goods," Econometrica, Econometric Society, vol. 48(6), pages 1487-1506, September.
    20. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    21. Chen, Yan & Plott, Charles R., 1996. "The Groves-Ledyard mechanism: An experimental study of institutional design," Journal of Public Economics, Elsevier, vol. 59(3), pages 335-364, March.
    22. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    23. Conlisk, John, 1973. "Quick Stability Checks and Matrix Norms," Economica, London School of Economics and Political Science, vol. 40(160), pages 402-409, November.
    24. Reichelstein, Stefan & Reiter, Stanley, 1988. "Game Forms with Minimal Message Spaces," Econometrica, Econometric Society, vol. 56(3), pages 661-692, May.
    25. Mathevet, Laurent A., 2010. "Supermodular mechanism design," Theoretical Economics, Econometric Society, vol. 5(3), September.
    26. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
    27. T. Tideman, 1983. "An experiment in the demand-revealing process," Public Choice, Springer, vol. 41(3), pages 387-401, January.
    28. Jordan, J. S., 1986. "Instability in the implementation of Walrasian allocations," Journal of Economic Theory, Elsevier, vol. 39(2), pages 301-328, August.
    29. Cason, Timothy N. & Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2006. "Secure implementation experiments: Do strategy-proof mechanisms really work?," Games and Economic Behavior, Elsevier, vol. 57(2), pages 206-235, November.
    30. Arifovic, Jasmina & Ledyard, John, 2011. "A behavioral model for mechanism design: Individual evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 374-395, May.
    31. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation for Research in Economics, Yale University.
    32. 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.
    33. Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
    34. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    35. Lin Zhou, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," Review of Economic Studies, Oxford University Press, vol. 58(1), pages 107-119.
    36. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June.
    37. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    38. Van Essen, Matthew J., 2008. "A Simple Supermodular Mechanism that Implements Lindahl Allocations," MPRA Paper 12781, University Library of Munich, Germany.
    39. Vega-Redondo, Fernando, 1989. "Implementation of Lindahl equilibrium: an integration of the static and dynamic approaches," Mathematical Social Sciences, Elsevier, vol. 18(3), pages 211-228, December.
    40. L. Hurwicz, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 217-225.
    41. Matt Van Essen, 2012. "Information complexity, punishment, and stability in two Nash efficient Lindahl mechanisms," Review of Economic Design, Springer;Society for Economic Design, vol. 16(1), pages 15-40, March.
    42. de Trenqualye, Pierre, 1989. "Stable implementation of Lindahl allocations," Economics Letters, Elsevier, vol. 29(4), pages 291-294.
    43. Healy, Paul J., 2006. "Learning dynamics for mechanism design: An experimental comparison of public goods mechanisms," Journal of Economic Theory, Elsevier, vol. 129(1), pages 114-149, July.
    44. Yan Chen, 2002. "A family of supermodular Nash mechanisms implementing Lindahl allocations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 773-790.
    45. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    46. Varian, Hal R, 1994. "A Solution to the Problem of Externalities When Agents Are Well-Informed," American Economic Review, American Economic Association, vol. 84(5), pages 1278-1293, December.
    47. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    48. 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.
    49. Glazer, Jacob & Rosenthal, Robert W, 1992. "A Note on Abreu-Matsushima Mechanisms," Econometrica, Econometric Society, vol. 60(6), pages 1435-1438, November.
    50. Mount, Kenneth & Reiter, Stanley, 1977. "Economic Environments for Which There Are Pareto Satisfactory Mechanisms," Econometrica, Econometric Society, vol. 45(4), pages 821-842, May.
    51. Tian, Guoqiang, 1990. "Completely feasible and continuous implementation of the Lindahl correspondence with a message space of minimal dimension," Journal of Economic Theory, Elsevier, vol. 51(2), pages 443-452, August.
    52. 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.
    53. Hurwicz, Leonid & Walker, Mark, 1990. "On the Generic Nonoptimality of Dominant-Strategy Allocation Mechanisms: A General Theorem That Includes Pure Exchange Economies," Econometrica, Econometric Society, vol. 58(3), pages 683-704, May.
    54. Hirota, Masayoshi, 1985. "Global stability in a class of markets with three commodities and three consumers," Journal of Economic Theory, Elsevier, vol. 36(1), pages 186-192, June.
    55. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Masuda, Takehito & Okano, Yoshitaka & Saijo, Tatsuyoshi, 2014. "The minimum approval mechanism implements the efficient public good allocation theoretically and experimentally," Games and Economic Behavior, Elsevier, vol. 83(C), pages 73-85.
    2. repec:dpr:wpaper:0874 is not listed on IDEAS
    3. Healy, Paul J. & Jain, Ritesh, 2017. "Generalized Groves–Ledyard mechanisms," Games and Economic Behavior, Elsevier, vol. 101(C), pages 204-217.
    4. Reischmann, Andreas, 2016. "Conditional Contribution Mechanisms for the Provision of Public Goods in Dynamic Settings - Theory and Experimental Evidence," Annual Conference 2016 (Augsburg): Demographic Change 145613, Verein für Socialpolitik / German Economic Association.
    5. Van Essen, Matthew & Walker, Mark, 2017. "A simple market-like allocation mechanism for public goods," Games and Economic Behavior, Elsevier, vol. 101(C), pages 6-19.
    6. Meng, Dawen & Tian, Guoqiang, 2013. "Entry-Deterring Nonlinear Pricing with Bounded Rationality," MPRA Paper 57935, University Library of Munich, Germany, revised May 2014.
    7. Arifovic, Jasmina & Ledyard, John, 2011. "A behavioral model for mechanism design: Individual evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 374-395, May.
    8. Matt Essen, 2014. "A Clarke tax tâtonnement that converges to the Lindahl allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 309-327, August.
    9. Matt Van Essen, 2015. "Bartering Games in the Kolm Triangle," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(3), pages 297-310, June.
    10. repec:dpr:wpaper:0874r is not listed on IDEAS
    11. Matt Van Essen, 2012. "A note on the stability of Chen’s Lindahl mechanism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 365-370, February.
    12. Matt Van Essen, 2012. "Information complexity, punishment, and stability in two Nash efficient Lindahl mechanisms," Review of Economic Design, Springer;Society for Economic Design, vol. 16(1), pages 15-40, March.
    13. Jacek B. Krawczyk & Mabel Tidball, 2016. "Economic Problems with Constraints: How Efficiency Relates to Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-19, December.

    More about this item

    Keywords

    Mechanism design; implementation; stability; learning;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:the:publsh:898. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Martin J. Osborne) or (Rebekah McClure). General contact details of provider: http://econtheory.org .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.