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Games On a Compact Set

Published online by Cambridge University Press:  20 November 2018

J. E. L. Peck
Affiliation:
McGill University
A. L. Dulmage
Affiliation:
Royal Military College of Canada
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Von Neumann's fundamental theorem of the theory of games has been extended by various authors and recently in two different directions by Kneser (8) and Nikaidô (9). We present here a form of the theorem, which is more general than that of both these authors. We develop some consequences of this theorem, which make it easier to decide whether certain classes of games have a value and we give several illustrative examples

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Berge, C., Sur une théorie ensembliste des jeux alternatifs, J. Math. Pure Appl., (9), 32 (1953), 129184.Google Scholar
2. Blackwell, D. and Girschick, M. A., Theory of games and statistical decisions (New York, 1954).Google Scholar
3. Choquet, A, Sur le théorème des point-selle de la théorie des jeux, Bull. Sci. Math., (2), 70 (1955), 4853.Google Scholar
4. Dulmage, A. L. and Peck, J. E. L., Certain infinite zero-sum two-person games, Can. J. Math., 5(1956), 412416.Google Scholar
5. Halmos, P. R., Measure Theory (New York, 1950).Google Scholar
6. Kakutani, S., Concrete representations of abstract (M)-spaces, Ann. of Math., 42 (1941), 9941024.Google Scholar
7. Karlin, S., Operator treatment of the minimax principle, Contributions to the theory of games, Ann. of Math. Studies, No. 24 (1950), 133154.Google Scholar
8. Kneser, H., Sur un théorème fondamental de la théorie des jeux, C.R. Acad. Sci. Paris, 234 (1952), 24182420.Google Scholar
9. Nikaidô, H., On a minimax theorem and its applications to functional analysis, J. Math. Soc. Japan, 5 (1953), 8694.Google Scholar
10. Pettis, B. J., Separation theorems for convex sets, Math. Mag. 29 (1956), 233245.Google Scholar
11. Ville, J., Sur la théorie générale des jeux ou intervient l'habilité des joueurs, Traité du Calcul des Probabilités et de ses Applications, E. Borei, etc., 4, 2 (1938), 105–113.Google Scholar
12. Wald, A., Generalization of a theorem by von Neumann concerning zero sum two person games, Ann. of Math. 46 (1945), 281286.Google Scholar
13. Wald, A., Foundations of a general theory of sequential decision functions, Econometrica, 15(1947), 279313.Google Scholar