Strategy Ah is dominated by strategy Ak, if ahj £akj for j=1,2,…,n.
Strategy Br is dominated by strategy Bs, if air ³ ais for i=1,2,…,m.
A strategy can be dominated also by a convex combination of some strategies, i. e. by a mixed strategy.
Strategy Ah is dominated by a mixed strategy x = (x1,x2, … xm), if
Strategy Br is dominated by a mixed strategy y = (y1,y2, … yn), if
In a game with the payoff matrix
first strategy of player B is dominated by his mixed strategy (0,1/2,1/2), since (1,3) ³ 0.5*(-1,5) + 0.5*(3,-3). The optimal solution of the given game is determined only by second and third strategy of player B as the following picture shows.