6. Calculating Mixed Strategy Nash Equilibrium of a 3 x 3 Game: An Example (Game Theory Playlist 4) 

Because the definition of dominance is when one strategy does at least as well as and in some cases strictly better than any other strategy no matter what the opposing player does. Taking this definition into mind then this means if we look at player 2. M dominates L because 4 > 3, 6 > 3, and 5 > 2. However for player 1 U does not dominate D because 10 > 7, 2 < 5, and 6 > 3. Here we see that while U does better than D in 2 cases (when player 2 chooses L and R) U does worse than D when player 2 chooses M. If U were 10 5 and 6 then it would dominate D because it would be 10 > 7, 5 = 5, and 6 > 3 so if that were the case then yes it would dominate D but it doesn't because 2 < 5. So considering that L is never going to be played by player 2 because it is strongly dominated by M, and no strategies for player 1 are dominant, each player is might be better off using a mixed strategy. But you'd have to calculate the expected payoffs. If we are talking about Pure Strategy then the best response is (U, M) payoff of (6,6).

Of course, this is part of the IESDS which applies for the mixed strategies too. If the mixed strategy has a better payoff for a player than the pure strategy , therefore one can eliminate the dominated strategy.