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This 1948 report presents a summary of zero-sum two-person games with a finite number of strategies as developed by von Neumann. However, Ville's proof of the fundamental theorem is given rather than the original proof of von Neumann. This is followed by the unpublished results on games with a finite number of strategies obtained by M.A. Girshick, O. Helmer, L.S. Shapley and R.N. Snow. Among the results on games with a continuum of strategies are those of H. Bohnenblust, M. Dresher, T.E. Harris, and J.C.C. McKinsey.

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