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Classification of Two-Person Ordinal Bimatrix Games

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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.

Suggested Citation

  • Imre Barany & J. Lee & Martin Shubik, 1991. "Classification of Two-Person Ordinal Bimatrix Games," Cowles Foundation Discussion Papers 996, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:996
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    Cited by:

    1. Martin Shubik, 2012. "A Web Gaming Facility for Research and Teaching," Cowles Foundation Discussion Papers 1860R, Cowles Foundation for Research in Economics, Yale University, revised Jun 2013.
    2. Stanford, William, 2004. "Individually rational pure strategies in large games," Games and Economic Behavior, Elsevier, vol. 47(1), pages 221-233, April.
    3. Xu, Chunhui, 2000. "Computation of noncooperative equilibria in ordinal games," European Journal of Operational Research, Elsevier, vol. 122(1), pages 115-122, April.
    4. 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.
    5. GERMANO, Fabrizio, 1998. "On Nash equivalence classes of generic normal form games," LIDAM Discussion Papers CORE 1998033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. 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.
    7. Richárd Kicsiny & Zoltán Varga, 2023. "New algorithm for checking Pareto optimality in bimatrix games," Annals of Operations Research, Springer, vol. 320(1), pages 235-259, January.
    8. 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

    Keywords

    Game theory; rationality; preferences;
    All these keywords.

    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

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