IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-01378460.html
   My bibliography  Save this paper

Implementation of the Lindahl Correspondance via Simple Indirect Mechanisms

Author

Listed:
  • Hassan Benchekroun

    (Department of Economics [Montréal] - McGill University = Université McGill [Montréal, Canada])

  • Charles Figuières

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Mabel Tidball

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

Our paper proposes an original angle to study the free-rider problem in the provision of public goods when the regulator has no information about agents' preferences. For a given outcome - specifically a Lindahl allocation - we ask what assumptions have to be imposed on simple mechanisms (in a precisely defined sense) that have the ability to Nash-implement it. Our answer lies in two main results: i) transfers necessarily belongs to a class of mechanisms that are linear in individual contributions to the public good, ii) there exists a subset of this class that fully implement Lindahl allocations. This subset encompasses, but does not reduce to, Walker (1981).

Suggested Citation

  • Hassan Benchekroun & Charles Figuières & Mabel Tidball, 2016. "Implementation of the Lindahl Correspondance via Simple Indirect Mechanisms," Working Papers halshs-01378460, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01378460
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01378460
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-01378460/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
    2. Bhaskar Dutta & Arunava Sen & Rajiv Vohra, 1994. "Nash implementation through elementary mechanisms in economic environments," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 173-203, December.
    3. Wolfgang Buchholz & Wolfgang Peters, 2007. "Justifying the Lindahl solution as an outcome of fair cooperation," Public Choice, Springer, vol. 133(1), pages 157-169, October.
    4. Bracht, Juergen & Figuieres, Charles & Ratto, Marisa, 2008. "Relative performance of two simple incentive mechanisms in a public goods experiment," Journal of Public Economics, Elsevier, vol. 92(1-2), pages 54-90, February.
    5. Cornes,Richard & Sandler,Todd, 1996. "The Theory of Externalities, Public Goods, and Club Goods," Cambridge Books, Cambridge University Press, number 9780521477185, September.
    6. Sébastien Rouillon, 2013. "Anonymous implementation of the Lindahl correspondence: possibility and impossibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1179-1203, April.
    7. repec:dau:papers:123456789/4809 is not listed on IDEAS
    8. Foley, Duncan K, 1970. "Lindahl's Solution and the Core of an Economy with Public Goods," Econometrica, Econometric Society, vol. 38(1), pages 66-72, January.
    9. Silvestre, Joaquim, 1984. "Voluntariness and efficiency in the provision of public goods," Journal of Public Economics, Elsevier, vol. 24(2), pages 249-256, July.
    10. Bezalel Peleg, 1996. "Double implementation of the Lindahl equilibrium by a continuous mechanism," Review of Economic Design, Springer;Society for Economic Design, vol. 2(1), pages 311-324, December.
    11. Oakland, William H., 1987. "Theory of public goods," Handbook of Public Economics, in: A. J. Auerbach & M. Feldstein (ed.), Handbook of Public Economics, edition 1, volume 2, chapter 9, pages 485-535, Elsevier.
    12. Shitovitz, Benyamin & Spiegel, Menahem, 1998. "Cournot-Nash and Lindahl Equilibria in Pure Public Good Economies," Journal of Economic Theory, Elsevier, vol. 83(1), pages 1-18, November.
    13. Estelle Midler & Charles Figuières & Marc Willinger, 2015. "Choice overload, coordination and inequality: three hurdles to the effectiveness of the compensation mechanism?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(3), pages 513-535, October.
    14. Van Essen, Matthew J., 2008. "A Simple Supermodular Mechanism that Implements Lindahl Allocations," MPRA Paper 12781, University Library of Munich, Germany.
    15. 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.
    16. L. Hurwicz, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 217-225.
    17. Hindriks, Jean & Myles, Gareth D., 2013. "Intermediate Public Economics," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262018691, April.
    18. Li, Qi & Nakamura, Shinsuke & Tian, Guoqiang, 1995. "Nash-Implementation of the Lindahl Correspondence with Decreasing Returns to Scale Technologies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(1), pages 37-52, February.
    19. 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.
    20. Falkinger, Josef, 1996. "Efficient private provision of public goods by rewarding deviations from average," Journal of Public Economics, Elsevier, vol. 62(3), pages 413-422, November.
    21. 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.
    22. Matthew J. Essen, 2013. "A Simple Supermodular Mechanism that Implements Lindahl Allocations," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(3), pages 363-377, June.
    23. 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.
    24. Iyengar, Sheena S. & Kamenica, Emir, 2010. "Choice proliferation, simplicity seeking, and asset allocation," Journal of Public Economics, Elsevier, vol. 94(7-8), pages 530-539, August.
    25. Guoqiang Tian, 1989. "Implementation of the Lindahl Correspondence by a Single-Valued, Feasible, and Continuous Mechanism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 613-621.
    26. Roberts, Donald John, 1974. "The Lindahl solution for economies with public goods," Journal of Public Economics, Elsevier, vol. 3(1), pages 23-42, February.
    27. Andrew Postlewaite & David Wettstein, 1989. "Feasible and Continuous Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 603-611.
    28. Luis Corchon & Simon Wilkie, 1996. "Double implementation of the ratio correspondence by a market mechanism," Review of Economic Design, Springer;Society for Economic Design, vol. 2(1), pages 325-337, December.
    29. Sato, Toshihiro, 1987. "Equity, fairness and lindahl equilibria," Journal of Public Economics, Elsevier, vol. 33(2), pages 261-271, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tian, Guoqiang, 2000. "Double implementation of linear cost share equilibrium allocations," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 175-189, September.
    2. Van Essen, Matthew J., 2008. "A Simple Supermodular Mechanism that Implements Lindahl Allocations," MPRA Paper 12781, University Library of Munich, Germany.
    3. Takuma Wakayama & Takehiko Yamato, 2023. "Comparison of the voluntary contribution and Pareto-efficient mechanisms under voluntary participation," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 517-553, June.
    4. 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.
    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. , J. & ,, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
    7. 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.
    8. 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.
    9. Sertel, Murat R. & Sanver, M. Remzi, 1999. "Equilibrium outcomes of Lindahl-endowment pretension games1," European Journal of Political Economy, Elsevier, vol. 15(2), pages 149-162, June.
    10. 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.
    11. Tian, Guoqiang, 2000. "Implementation of balanced linear cost share equilibrium solution in Nash and strong Nash equilibria," Journal of Public Economics, Elsevier, vol. 76(2), pages 239-261, May.
    12. Tian, Guoqiang, 2009. "Implementation of Pareto efficient allocations," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 113-123, January.
    13. Sébastien Rouillon, 2013. "Anonymous implementation of the Lindahl correspondence: possibility and impossibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1179-1203, April.
    14. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    15. Thomson, William, 2005. "Divide-and-permute," Games and Economic Behavior, Elsevier, vol. 52(1), pages 186-200, July.
    16. Charles Figuières & Marc Willinger, 2012. "Regulating ambient pollution when social costs are unknown," Working Papers 12-17, LAMETA, Universtiy of Montpellier, revised Jun 2012.
    17. Tymon Słoczyński, 2012. "Zastosowanie zasady równych ofiar do oceny sprawiedliwości taryfy podatku dochodowego od osób fizycznych (PIT) w Polsce," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 10, pages 23-47.
    18. 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.
    19. Sébastien ROUILLON, 2009. "A new mechanism to implement the Lindahl equilibriums (In French)," Cahiers du GREThA (2007-2019) 2009-09, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    20. Luis Corchon & Simon Wilkie, 1996. "Double implementation of the ratio correspondence by a market mechanism," Review of Economic Design, Springer;Society for Economic Design, vol. 2(1), pages 325-337, December.

    More about this item

    Keywords

    Lindahl allocations; mechanism design;

    JEL classification:

    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:hal:wpaper:halshs-01378460. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.