Classification of Two-Person Ordinal Bimatrix Games
AbstractThe 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.
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Bibliographic InfoArticle provided by Springer in its journal International Journal of Game Theory.
Volume (Year): 21 (1992)
Issue (Month): 3 ()
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Web page: http://link.springer.de/link/service/journals/00182/index.htm
Other versions of this item:
- 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.
- 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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- Fabrizio Germano, 2003.
"On some geometry and equivalence classes of normal form games,"
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- Stanford, William, 2004. "Individually rational pure strategies in large games," Games and Economic Behavior, Elsevier, vol. 47(1), pages 221-233, April.
- 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.
- 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).
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