Abstract
This paper characterizes some class of matrices with rows and columns having properties closely related to the convexity-concavity of functions. The matrix games described by such payoff matrices well approximate continuous games on the unit square with payoff functions F(x,y) concave in x for each y, and convex in y for each x. It is shown that the optimal strategies in such matrix games have a very simple structure and a search-procedure is given. The results have a very close relationship with the results of papers: Debreu (1952), Glicksberg (1952), Radzik (1991, 1992,1993) and Shapley (1964).
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