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.
Bárány, Imre; Lee, Jon; and Shubik, Martin, "Classification of Two-Person Ordinal Bimatrix Games" (1991). Cowles Foundation Discussion Papers. 1239.