IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v21y1992i3p267-90.html
   My bibliography  Save this article

Classification of Two-Person Ordinal Bimatrix Games

Author

Listed:
  • Barany, I
  • Lee, J
  • Shubik, M

Abstract

The set of possible outcomes of a strongly ordinal bimatrix game is studied by imbedding each pair of possible payoffs as a point on the standard two-dimensional integral lattice. In particular, we count the number of different Pareto optimal sets of each cardinality; we establish asymptotic bounds for the number of different convex hulls of the point sets, for the average shape of the set of points dominated by the Pareto optimal set, and for the average shape of the convex hull of the point set. We also indicate the effect of individual rationality considerations on our results. As most of our results are asymptotic, the appendix includes a careful examination of the important case of 2 x 2 games.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Barany, I & Lee, J & Shubik, M, 1992. "Classification of Two-Person Ordinal Bimatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 267-290.
  • Handle: RePEc:spr:jogath:v:21:y:1992:i:3:p:267-90
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    Citations

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


    Cited by:

    1. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 561-581, November.
    2. GERMANO, Fabrizio, 1998. "On Nash equivalence classes of generic normal form games," CORE Discussion Papers 1998033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Stanford, William, 2004. "Individually rational pure strategies in large games," Games and Economic Behavior, Elsevier, vol. 47(1), pages 221-233, April.
    4. Thomas Quint & Martin Shubik & Dickey Yan, 1995. "Dumb Bugs and Bright Noncooperative Players: Games, Context and Behavior," Cowles Foundation Discussion Papers 1094, Cowles Foundation for Research in Economics, Yale University.
    5. Xu, Chunhui, 2000. "Computation of noncooperative equilibria in ordinal games," European Journal of Operational Research, Elsevier, vol. 122(1), pages 115-122, April.
    6. Thomas Quint & Martin Shubik, 1994. "On the Number of Nash Equilibria in a Bimatrix Game," Cowles Foundation Discussion Papers 1089, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

    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:spr:jogath:v:21:y:1992:i:3:p:267-90. 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: http://www.springer.com .

    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.