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The Elementary Theory of Convex Polyhedra
Elementary Proof of a Minimax Theorem due to von Neumann
Basic Solutions of Discrete Games
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1)-dimensional ANNALS OF MATHEMATICS Banach space basic solution behavior Bohnenblust bounding face coefficients columns compact completely mixed condition contains convergence convex closure convex cone convex polyhedron convex set COROLLARY corresponding Cowles Commission defined definition denote dimension dimensional distributions elements equations essential game exists extreme solutions extreme support finite number follows functions fundamental theorem Gale game in reduced game matrix given halfspace hence holds hyperplane hypothesis implies imputation inequalities infinite games intersection isomorphic Karlin kernel Kuhn Lemma linearly independent Morgenstern n game Neumann non-negative obtained optimal mixed strategies optimal strategies payoff payoff matrix plane play player polyhedral cone polynomial game positive PROOF pure strategies real number respectively rows S-equivalent satisfies sequence sets of optimal Shapley simplex skew-symmetric matrix strategic equivalence strategies X submatrix subset supporting hyperplane symmetric game theory of games topology Tucker two-person games vectors Wald weakly y-player zero zero-sum