Geodesic
On the Metric Approach in the Theory of Matrix Games
Contributions to game theory and management, Tome 3 (2010), pp. 22-28.

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It is considered the problem connected with the combinatorial metric approach to the notion of solution of matrix games. According to this approach it is searched a matrix $B$ that possesses equilibrium and is the closest to the given matrix $A$ in the sense of some metric $d(A, B).$ In the case when $d(A,B)$ is the number of pairs $(i,j)$ such that $a_{ij} \neq b_{ij}$ it is established some properties of the quantity $\max_A\min_B d(A,B)$.
Keywords: matrix game, equilibrium situation, metrics, combinatorial approach. 
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Аbdulla A. Azamov. On the Metric Approach in the Theory of Matrix Games. Contributions to game theory and management, Tome 3 (2010), pp. 22-28. http://geodesic.mathdoc.fr/item/CGTM_2010_3_a2/

[1] Neumann J., Morgenstern O., Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944 | MR | Zbl

[2] Karlin S., Mathematical Methods and Theory in Games, Programming and Economics, v. 1, Matrix Games, Programming and Mathematical Economics, Addison-Wesley, Reading–London, 1959, 433 pp. | MR

[3] Vorobyov N. N., “A Morden Game Theory”, Successes of Mathematical Sciences, 15:2 (1970), 80–140 (in Russian)

[4] Petrosyan L. A., Zenkevich N. A., Game Theory, World Scientific Publishing Co. Pte. Ltd., Singapore, 1996 (in Russian) | MR | Zbl

[5] Prasad K., “Observation, Measurement, and Computation in Finite Games”, International Journal of Game Theory, 32:4 (2004), 455–470 | DOI | MR | Zbl

[6] Azamov A., “On a combinatorial problem of matrix game theory”, Actual Problems of Control Theory and Mathematical modelling, Collected works, Fan, Tashkent, 1998, 4–8 (in Russian)

[7] Azamov A., “Combinatorial Approach to Theory of Matrix Games”, Uzbek Mathematical Journal, 2 (2004), 12–16 | MR

[8] Luce R. D., Raiffa H., Games and decisions, Foreign literature, M., 1961 | MR