IDEAS home Printed from
   My bibliography  Save this paper

How to use Rosen's normalised equilibrium to enforce a socially desirable Pareto efficient solution


  • Jacek B. Krawczyk
  • Mabel Tidball


We consider a situation, in which a regulator believes that constraining a complex good created jointly by competitive agents, is socially desirable. Individual levels of outputs that generate the constrained amount of the externality can be computed as a Pareto efficient solution of the agents' joint utility maximisation problem. However, generically, a Pareto efficient solution is not an equilibrium. We suggest the regulator calculates a Nash-Rosen coupled-constraint equilibrium (or a “generalised” Nash equilibrium) and uses the coupled-constraint Lagrange multiplier to formulate a threat, under which the agents will play a decoupled Nash game. An equilibrium of this game will possibly coincide with the Pareto efficient solution. We focus on situations when the constraints are saturated and examine, under which conditions a match between an equilibrium and a Pareto solution is possible. We illustrate our findings using a model for a coordination problem, in which firms' outputs depend on each other and where the output levels are important for the regulator.

Suggested Citation

  • Jacek B. Krawczyk & Mabel Tidball, 2009. "How to use Rosen's normalised equilibrium to enforce a socially desirable Pareto efficient solution," Working Papers 09-20, LAMETA, Universtiy of Montpellier, revised Jan 2011.
  • Handle: RePEc:lam:wpaper:09-20

    Download full text from publisher

    File URL:
    File Function: First version, 2009
    Download Restriction: no

    References listed on IDEAS

    1. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 817-868.
    2. Falk, Armin & Fischbacher, Urs, 2006. "A theory of reciprocity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 293-315, February.
    3. Bonein, Aurélie & Serra, Daniel, 2007. "Another experimental look at reciprocal behavior: indirect reciprocity," MPRA Paper 3257, University Library of Munich, Germany, revised Mar 2007.
    4. Kohler, Stefan, 2011. "Altruism and fairness in experimental decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 80(1), pages 101-109.
    5. Dufwenberg, Martin & Kirchsteiger, Georg, 2004. "A theory of sequential reciprocity," Games and Economic Behavior, Elsevier, vol. 47(2), pages 268-298, May.
    6. Jordi Brandts & Gary Charness, 2000. "Hot vs. Cold: Sequential Responses and Preference Stability in Experimental Games," Experimental Economics, Springer;Economic Science Association, vol. 2(3), pages 227-238, March.
    7. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
    8. Bethwaite, Judy & Tompkinson, Paul, 1996. "The ultimatum game and non-selfish utility functions," Journal of Economic Psychology, Elsevier, vol. 17(2), pages 259-271, April.
    9. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    10. Hill, Sarah A. & Neilson, William, 2007. "Inequality aversion and diminishing sensitivity," Journal of Economic Psychology, Elsevier, vol. 28(2), pages 143-153, April.
    11. Gary Bolton & Axel Ockenfels, 2005. "A stress test of fairness measures in models of social utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 957-982, June.
    12. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Boucekkine, Raouf & Krawczyk, Jacek B. & Vallée, Thomas, 2010. "Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1813-1835, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:lam:wpaper:09-20. 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: (Patricia Modat). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.