Abstract
The set of all linear spaces of continuous two-person zero-sum games on the unit square with pure equilibrium points is considered. It is shown that the set contains maximal linear spaces of any finite dimension greater than three.
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REFERENCES
Isaacs, R., Differential Games, New York–London–Sydney: John Wiley and Sons, 1965. Translated under the title: Differentsial’nye igry., Moscow: Mir, 1967.
Nash, J., Noncooperative games, in Matrichnye igry (Matrix Games), Moscow: Fizmatgiz, 1961, pp. 205–221.
Sobolev, A.I., On the dimension of the linear space of matrix games with a saddle point, in Uspekhi teorii igr (Advances in Game Theory), Vilnius: Mintis, 1975, pp. 66–68.
Aumann, R. and Maschler, M., Repeated Games with Incomplete Information, Cambridge, MA–London: MIT Press, 1995.
Harsanyi, J., Games with incomplete information played by Bayesian players, Manage. Sci., 1968, vol. 14, pp. 486–502.
Kreps, V., On maximal vector spaces of finite non-cooperative games, Int. Game Theory Rev., 2017, vol. 19. I.2.
Funding
The research was carried out within the framework of the Program of Basic Scientific Research of State Academies of Sciences for 2013–2020 (IREP RAS, article 169) and the Program of Basic Research of the National Research University Higher School of Economics in 2020.
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Translated by V. Potapchouck
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Kreps, V.L. Linear Spaces of Games on the Unit Square with Pure Equilibrium Points. Autom Remote Control 82, 1966–1975 (2021). https://doi.org/10.1134/S0005117921110114
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DOI: https://doi.org/10.1134/S0005117921110114