Polymatrix games and optimization problems

Consideration was given to the properties of the polymatrix game, a finite noncooperative game of $N$ players ($N\geqslant3$). A theorem of reduction of the search for Nash equilibria to an optimization problem was proved. This clears the way to the numerical search of equilibria. Additionally, a simple proof of the Nash theorem of existence of equilibrium in the polymatrix game was given using the theorem of existence of solution in the optimization problem.

Presented by the member of Editorial Board: A. I. Kibzun