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Existence theorems of Nash equilibria for non-cooperative \(n\)-person games. (English) Zbl 0837.90126
Summary: We first obtain existence theorems of Nash equilibria for non-cooperative \(n\)-person games which generalize a corresponding result of Nikaido and Isoda (1955). As applications, we give two new existence theorems of \(\varepsilon\)-equilibrium points which generalize that of Tijs (1981). Finally, a saddle point theorem of Komiya (1986) is deduced from one of our existence theorems of \(\varepsilon\)-equilibrium points.

91A10 Noncooperative games
Full Text: DOI
[1] Aubin JP (1982) Mathematical methods of game theory and economic theory. North-Holland Amsterdam
[2] Browder FE (1968) The fixed point theory of multi-valued mappings in topological vector spaces. Math Ann 177: 283-302 · Zbl 0176.45204 · doi:10.1007/BF01350721
[3] Fan K (1972) Minimax inequality and application, in Inequalities III. Shisha O (Ed) Academic Press New York
[4] Komiya H (1986) Coincidence theorem and a saddle point theorem. Proc Amer Math Soc 96: 599-602 · Zbl 0657.47055 · doi:10.1090/S0002-9939-1986-0826487-0
[5] Nikaido H, Isoda K (1955) Note on non-cooperative games. Pacific J Math 5: 807-815 · Zbl 0171.40903
[6] Tijs SH (1981) Nash equilibria for noncooperative n-person game in normal form. SIAM Review 23: 225-237 · Zbl 0456.90091 · doi:10.1137/1023038
[7] Rudin W (1973) Functional analysis. McGraw-Hill New York · Zbl 0253.46001
[8] Tan KK, Yu J (1994) A new minimax inequality with applications to existence theorems of equilibrium points. J Optim Theory Appl 82: 105-120 · Zbl 0819.46004 · doi:10.1007/BF02191782
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