IDEAS home Printed from
   My bibliography  Save this article

The relative interior of the base polyhedron and the core


  • Jingang Zhao

    () (Department of Economics, Iowa State University, 260 Heady Hall, Ames, IA 50011-1070, USA)


This note provides two necessary and sufficient conditions for the relative interior of the core (and the base polyhedron) to be non-empty: (i) the second largest excess of the prenucleolus is negative; (ii) the grand coalition's payoff is greater than the minimum no-blocking payoff. Such conditions imply an intuitive method in proving core existence, they also imply results on the sensitivity of the base polyhedron and the core.

Suggested Citation

  • Jingang Zhao, 2001. "The relative interior of the base polyhedron and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 635-648.
  • Handle: RePEc:spr:joecth:v:18:y:2001:i:3:p:635-648 Note: Received: June 25, 1999; revised version: May 8, 2000

    Download full text from publisher

    File URL:
    Download Restriction: Access to the full text of the articles in this series is restricted

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Ngo Van Long & Antoine Soubeyran, 2001. "Emission Taxes and Standards for an Asymmetric Oligopoly," CIRANO Working Papers 2001s-07, CIRANO.
    2. Long, Ngo Van & Soubeyran, Antoine, 2001. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 505-533, May.
    3. Browning, Edgar K, 1976. "The Marginal Cost of Public Funds," Journal of Political Economy, University of Chicago Press, vol. 84(2), pages 283-298, April.
    4. Van Long, Ngo & Soubeyran, Antoine, 2000. "Existence and uniqueness of Cournot equilibrium: a contraction mapping approach," Economics Letters, Elsevier, vol. 67(3), pages 345-348, June.
    5. Gérard Gaudet & Stephen W. Salant, 1991. "Uniqueness of Cournot Equilibrium: New Results From Old Methods," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 399-404.
    6. Collie, David, 1993. "Strategic trade policy under asymmetric oligopoly," European Journal of Political Economy, Elsevier, vol. 9(2), pages 275-280, May.
    7. Ngo, Van Long & Soubeyran, Antoine, 1997. "Cost heterogeneity, industry concentration and strategic trade policies," Journal of International Economics, Elsevier, vol. 43(1-2), pages 207-220, August.
    8. Buchanan, James M, 1969. "External Diseconomies, Corrective Taxes, and Market Structure," American Economic Review, American Economic Association, vol. 59(1), pages 174-177, March.
    9. Hoel, Michael, 1993. "Intertemporal properties of an international carbon tax," Resource and Energy Economics, Elsevier, vol. 15(1), pages 51-70, March.
    10. Van Long, N. & Soubeyran, A., 1997. "Cost Manipulation in Oligopoly: A Duality Approach," ASSET - Instituto De Economia Publica 174, ASSET (Association of Southern European Economic Theorists).
    11. Baumol,William J. & Oates,Wallace E., 1988. "The Theory of Environmental Policy," Cambridge Books, Cambridge University Press, number 9780521322249, March.
    12. Hansson, Ingemar & Stuart, Charles, 1985. "Tax revenue and the marginal cost of public funds in Sweden," Journal of Public Economics, Elsevier, vol. 27(3), pages 331-353, August.
    13. Nathalie de Marcellis-Warin & Erwann Michel-Kerjan, 2001. "The Public-Private Sector Risk-Sharing in the French Insurance "Cat. Nat. System"""," CIRANO Working Papers 2001s-60, CIRANO.
    14. Rauscher, Michael, 1997. "International Trade, Factor Movements, and the Environment," OUP Catalogue, Oxford University Press, number 9780198290506, June.
    15. Van Long, N. & Soubeyran, A., 1997. "Cost Manipulation in an Asymmetric Oligopoly: The Taxation Problem," ASSET - Instituto De Economia Publica 173, ASSET (Association of Southern European Economic Theorists).
    16. Benchekroun, Hassan & van Long, Ngo, 1998. "Efficiency inducing taxation for polluting oligopolists," Journal of Public Economics, Elsevier, vol. 70(2), pages 325-342, November.
    17. Greg Shaffer & Stephen W. Salant, 1999. "Unequal Treatment of Identical Agents in Cournot Equilibrium," American Economic Review, American Economic Association, vol. 89(3), pages 585-604, June.
    18. Ulph, Alistair, 1996. "Environmental Policy and International Trade when Governments and Producers Act Strategically," Journal of Environmental Economics and Management, Elsevier, vol. 30(3), pages 265-281, May.
    19. Conrad Klaus, 1993. "Taxes and Subsidies for Pollution-Intensive Industries as Trade Policy," Journal of Environmental Economics and Management, Elsevier, vol. 25(2), pages 121-135, September.
    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. Takayuki Watanabe & Nobuo Matsubayashi, 2013. "Note on Stable Mergers in a Market with Asymmetric Substitutability," Economics Bulletin, AccessEcon, vol. 33(3), pages 2024-2033.
    2. repec:spr:etbull:v:5:y:2017:i:2:d:10.1007_s40505-017-0115-6 is not listed on IDEAS
    3. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
    4. Jingang Zhao, 2009. "Estimating Merging Costs by Merger Preconditions," Theory and Decision, Springer, vol. 66(4), pages 373-399, April.

    More about this item


    Base polyhedron; Core; Minimum no-blocking payoff; Nucleolus; Sensitivity analysis.;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations


    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:spr:joecth:v:18:y:2001:i:3:p:635-648. 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: (Sonal Shukla) or (Rebekah McClure). 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.