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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 games 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 2×2 games.

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Authors and Affiliations

  1. Cowless Foundation for Research in Economics and the Department of Operations Research at Yale University, USA

    I. Bárány

  2. The Courant Institute of Mathematical Sciences at New York University, USA

    I. Bárány

  3. The Mathematical Institute of the Hungarian Academy of Sciences, Hungary

    I. Bárány

  4. Department of Operations Research, Yale University, 1 Hillhouse Avenue, Third Floor, 06520, New Haven, Connecticut, USA

    J. Lee

  5. Cowles Foundation for Research in Economics and the Department of Operations Research at Yale University, USA

    M. Shubik

Authors
  1. I. Bárány
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  2. J. Lee
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  3. M. Shubik
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Additional information

Supported by the Program in Discrete Mathematics and its Applications at Yale and NSF Grant CCR-8901484.

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Bárány, I., Lee, J. & Shubik, M. Classification of two-person ordinal bimatrix games. Int J Game Theory 21, 267–290 (1992). https://doi.org/10.1007/BF01258279

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  • DOI: https://doi.org/10.1007/BF01258279

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