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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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ANNALS OF MATHEMATICS assume Banach space basic solutions behavior Bohnenblust choose coalition columns compact components condition cone consider contains continuous continuous functions converges convex cone convex set COROLLARY corresponding defined definition denote dF(x dimension dimensional distribution elements equations essential exists extreme support finite number follows function given halfspace hence hyperplane hypothesis implies imputation inequalities infinite games information set integral interior intersection isomorphic Karlin kernel Kuhn Lemma linear mapping matrix Morgenstern move n game n-person game n-tuple Neumann non-negative obtained optimal mixed strategies optimal strategies payoff payoff matrix perfect information plane play polyhedral positive Princeton PROOF properties pure strategies rows satisfies sequence sets of optimal Shapley signaling strategy simplex space strategies X strategy for player subgame subset supporting hyperplane Suppose symmetric game Theory of Games tion topology unit interval vector zero