## Contributions to the theory of games, Volume 1 |

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### Contents

The Elementary Theory of Convex Polyhedra | 3 |

Elementary Proof of a Minimax Theorem due to von Neumann | 19 |

Basic Solutions of Discrete Games | 27 |

12 other sections not shown

### Common terms and phrases

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