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Probability and possibility models of matrix games of two subjects

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Abstract

Probability models and their possibility counterparts of one-matrix and bimatrix games of two subjects (A and B) were defined and analyzed. For the one-matrix game possibility model, a theorem was proven saying that maximin and minimax fuzzy strategies exist and that possibilities of A winning or losing (B) in relation to these strategies are equal. The concepts of fuzzy and randomized game strategies were defined and analyzed. The problem of statistic modeling of A and B fuzzy strategies was resolved. For possible models of bimatrix games, the existence of equilibrium points was examined. For the problem of maximization of the winning A and B possibility, it was proven that equilibrium points exist. For the problem of minimizing the possibility of losses, it was shown that if equilibrium points exist, some of them are related to clear strategies, A and B.

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Authors and Affiliations

  1. Computer Methods in Physics, Faculty of Physics Moscow State University, Moscow, Russia

    S. S. Papilin & Yu. P. Pyt’ev

Authors
  1. S. S. Papilin
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  2. Yu. P. Pyt’ev
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Correspondence to S. S. Papilin.

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Original Russian Text © S.S. Papilin, Yu.P. Pyt’ev, 2010, published in Matematicheskoe Modelirovanie, 2010, Vol. 22, No. 12, pp. 144–160.

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Papilin, S.S., Pyt’ev, Y.P. Probability and possibility models of matrix games of two subjects. Math Models Comput Simul 3, 528–540 (2011). https://doi.org/10.1134/S2070048211040077

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  • DOI: https://doi.org/10.1134/S2070048211040077

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