Let us consider a game with a payoff matrix

and with optimal strategies of players **x**_{0}, **y**_{0}. Under the assumption that the game has no saddle point, both components of the vector **y**_{0 } are positive and therefore the following equations hold: *E*(**x**_{0},B_{1})=*v*, *E*(**x**_{0},B_{2})=*v* (these equations follow from the equivalence of a matrix game to a linear programming problem and from relationships between solutions of primal and dual problems). Since *E*(**x**_{0},B_{1})=*a*_{11}*x*_{01}+*a*_{21}*x*_{02}, *E*(**x**_{0},B_{2})=* a*_{12}*x*_{01}+*a*_{22}*x*_{02}, the following equation is valid: *a*_{11}*x*_{01}+*a*_{21}*x*_{02 }=* a*_{12}*x*_{01}+*a*_{22}*x*_{02.} After the substitution *x*_{02 }=*1- x*_{01} ,* * the solution to this equation yields the following:

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