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Certain Infinite Zero-Sum Two-Person Games

Published online by Cambridge University Press:  20 November 2018

A. L. Dulmage  and
J. E. L. Peck
A. L. Dulmage
Affiliation:
Royal Military College of Canada
J. E. L. Peck
Affiliation:
University of New Brunswick
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1. Introduction. The theorem of von Neumann, that every finite, zero-sum two-person game has a value, has been extended in various ways to infinite games. In particular Wald (6) has shown that any bounded game in which one player has finitely many pure strategies, has a value. Our interest was aroused by the infinite analogue of the game of “hide and seek” as described by von Neumann (5), which does not appear to fit any of the known cases, unless the matrix is bounded.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 412 - 416
Copyright
Copyright © Canadian Mathematical Society 1956

References

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5. von Neumann, J., A certain zero-sum two-person game equivalent to the optimal assignment problem, Ann. Math. Studies, 28 (1953), 5–12.Google Scholar
6. Wald, A., Generalization of a theorem by v. Neumann concerning zero sum two person games, Ann. Math., 46 (1945), 281–286.Google Scholar