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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d09b/d0996.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 996.

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Length: 26 pages
Date of creation: Oct 1991
Date of revision:
Publication status: Published in International Journal of Game Theory (1992), 21(3): 267-290
Handle: RePEc:cwl:cwldpp:996

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Game theory; rationality; preferences;

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Cited by:
  1. Stanford, William, 2004. "Individually rational pure strategies in large games," Games and Economic Behavior, Elsevier, vol. 47(1), pages 221-233, April.
  2. 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.
  3. 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.
  4. Xu, Chunhui, 2000. "Computation of noncooperative equilibria in ordinal games," European Journal of Operational Research, Elsevier, vol. 122(1), pages 115-122, April.
  5. 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).
  6. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer, vol. 34(4), pages 561-581, November.

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