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On computational search for Nash equilibrium in hexamatrix games. (English) Zbl 1336.91010
Summary: The problem of numerical finding of a Nash equilibrium in a 3-player polymatrix game is considered. Such a game can be completely described by six matrices, and it turns out to be equivalent to the solving a nonconvex optimization problem with a bilinear structure in the objective function. Special methods of local and global search for the optimization problem are proposed and investigated. The results of computational solution of the test game are presented and analyzed.

##### MSC:
 91A06 $$n$$-person games, $$n>2$$ 91A10 Noncooperative games 91-08 Computational methods for problems pertaining to game theory, economics, and finance 90C26 Nonconvex programming, global optimization
Matlab
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