Abstract
In the theory of zero-sum, two-person games the basic theorem was proved by John von Neumann; he used the Brouwer fixed-point theorem. In the theory of many-person games the basic theorem was proved by J. F. Nash; he also used the Brouwer fixed-point theorem. We will prove Nash’s theorem with the Kakutani fixed-point theorem.
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Franklin, J. (1980). Fixed-Point Theorems. In: Methods of Mathematical Economics. Undergraduate Texts in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25317-5_3
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DOI: https://doi.org/10.1007/978-3-662-25317-5_3
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