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Yet Another Proof of the Minimax Theorem

Published online by Cambridge University Press:  20 November 2018

J.E.L. Peck
J.E.L. Peck*
Affiliation:
McGill University
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There are so many proofs of this theorem in the literature, that an excuse is necessary before exhibiting another. Such may be found by examining the proof given below for the following: it uses no matrices, almost no topology and makes little use of the geometry of convex sets; it applies equally well to the case where only one of the pure strategy spaces is finite; also there is no assumption that the payoff function is bounded. Thus it can provide a short route to the more general forms of the theorem.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 1 , Issue 2 , May 1958 , pp. 97 - 100
Copyright
Copyright © Canadian Mathematical Society 1958

References

Dantzig, G.B., Constructive proof of the min-max theorem, Pacific J. Math. 6(1956), 25-33.Google Scholar
Fan, K., Minimax theorems, Proc. Nat. Acad. Sci. 39 (1953), 42-47.Google Scholar
Kuhn, H.W., Lectures on the theory of games, (Princeton University, 1953).Google Scholar
Peck, J.E.L., and Dulmage, A.L., Games on a compact set, Canadian J. Math. 9(1957), 450-458.Google Scholar
Wald, A., Generalization of a theorem by von Neumann, Ann. of Math. 46 (1945), 281-286.Google Scholar
Zieba, A., An elementary proof of the minimax theorem. Colloquium Math. 4 (1957), 224-226.Google Scholar