Dominance of Strategies

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

Example

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.