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Classification of Two-Person Ordinal Bimatrix Games

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  • 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.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 21 (1992)
Issue (Month): 3 ()
Pages: 267-90

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Handle: RePEc:spr:jogath:v:21:y:1992:i:3:p:267-90

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Cited by:
  1. 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.
  2. Fabrizio Germano, 2003. "On Some Geometry and Equivalence Classes of Normal Form Games," Working Papers 42, Barcelona Graduate School of Economics.
  3. Xu, Chunhui, 2000. "Computation of noncooperative equilibria in ordinal games," European Journal of Operational Research, Elsevier, Elsevier, vol. 122(1), pages 115-122, April.
  4. GERMANO, Fabrizio, 1998. "On Nash equivalence classes of generic normal form games," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1998033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Stanford, William, 2004. "Individually rational pure strategies in large games," Games and Economic Behavior, Elsevier, vol. 47(1), pages 221-233, April.
  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.

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