Minimax Theory and its Applications 09 (2024), No. 2, 287--304
Copyright Heldermann Verlag 2024
Some Qualitative Properties of Matrix Two-Person Games
Duong Thi Kim Huyen
Department of Mathematics, Hanoi Pedagogical University 2, Vinh Phuc, Vietnam
duongthikimhuyen@hpu2.edu.vn
Nguyen Dong Yen
Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
ndyen@math.ac.vn
This paper studies some qualitative aspects of matrix two-person games. The continuity of the characteristic sets and of the value of the games are established under suitable conditions. The upper semicontinuity of the characteristic sets and the density of the games having a unique optimal strategy for one player are obtained for matrix games of dimension 2 × 2. For further investigations, four open questions are formulated.
Keywords: Matrix two-person game, mixed strategy, linear program, characteristic set map, value of the game function, characteristic number, density.
MSC: 91A05, 91A10, 90C05, 49J53.
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