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References
For general reference in mathematics, the reader may want to consult Halmos (1950), Kelley (1955) and Kelley and Namioka (1963); and on minmax theorems, Parthasarathy and Raghavan (1971).
Aumann RJ (1964) Mixed and behavioural strategies in infinite extensive games. In: Dresher, Shapley, Tucker (eds), pp 627–650
Bourbaki N (1959) Eléments de mathematique, Livre VI: Intégration, Ch. VI: Intégration vectorielle. Hermann, Paris
Dresher M, Tucker AW, Wolfe P (eds) (1957) Contributions to the theory of games III (Annals of Mathematical Studies, vol 39). Princeton University Press, Princeton, New Jersey
Dresher M, Shapley LS, Tucker AW (eds) (1964) Advances in game theory (Annals of Mathematical Studies, vol 52). Princeton University Press, Princeton, New Jersey
Dubins L, Savage LJ (1965) How to gamble if you must. MacGraw Hill, New York
Grothendieck A (1952) Critères de compacité dans les espaces fonctionnels généraux. American Journal of Mathematics 74:168–186
Grothendieck A (1953) Sur less applications linéaires faiblement compactes d'espaces de type C(K). Canadian Journal of Mathematics 5:129–173
Halmos PR (1950) Measure theory. Van Nostrand, New York
Karlin S (1950) Operator treatment of the minmax principle, I. In: Kuhn HW, Tucker AW (eds), pp 133–154
Karlin S (1959) Mathematical methods and theory in games, programming and economics, vol II. Addison-Wesley
Kelley JL (1955) General topology. Van Nostrand, New York
Kelley JL, Namioka I, et al (1963) Linear topological spaces. Van Nostrand, New York
Kneser H (1952) Sur un théorème fondamental de la théorie des jeux. Comptes Rendus de l'Académie des Sciences 234:2418–2420
Kuhn HW, Tucker AW (eds) (1950) Contributions to the theory of games, I (Ann Math Studies, vol 24). Princeton University Press, Princeton, New Jersey
Nikaido H (1954) On von Neumann's minimax theorem. Pacific Journal of Mathematics 4:65–72
Parthasarathy T, Raghavan TES (1971) Some topics in two-person games. American Elsevier Publishing Company, New York
Restrepo R (1957) Tactical problems involving several actions. In: Dresher, Tucker, Wolfe (eds), pp 313–337
Sion M (1958) On general minimax theorems. Pacific Journal of Mathematics 8:171–176
Sion M, Wolfe P (1957) On a game without a value. In: Dresher, Tucker, Wolfe (eds), pp 299–305
Teh Tjoe-Tie (1963) Minmax theorems on conditionally compact sets. Annals of Mathematical Statistics 34:1536–1540
Wald A (1945) Generalization of a theorem by von Neumann concerning zero-sum two-person games. Annals of Mathematics 46:281–286
Wald A (1950) Note on zero-sum two-person games. Annals of Mathematics 52:739–742
Waternaux C (1983) Minmax and maxmin of repeated games without a recursive structure. CORE Discussion Paper 8313, Université Catholique de Louvain
Yanovskaya EB (1964) Minimax theorems for games on the unit square. Theory of Probability and its Applications 9:500–502
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This research was supported in part by the National Science Foundation Grant SES 8201373 and in part by the Office of Naval Research Contract ONR-N00014-79-C-0685 at the Institute for Mathematical Studies in the Social Sciences, Stanford University.
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Mertens, J.F. The minmax theorem for U.S.C.-L.S.C. payoff functions. Int J Game Theory 15, 237–250 (1986). https://doi.org/10.1007/BF01769388
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DOI: https://doi.org/10.1007/BF01769388