The principle of dominance can be used to reduce the size of games by eliminating strategies that would never be played. A strategy for a player is said to be dominated if the player can always do as well or better playing another strategy. Any dominated strategy can be eliminated from the game. In other words, a strategy can be eliminated if all its game outcomes are the same as or worse than the corresponding game outcomes of another strategy.

Using the principle of dominance, we reduce the size of the following game:

In this game, $X_3$ will never be played because X can always do better by playing $X_1$ or $X_2$. The new game is

Here is another example:

In this game, Y would never play $Y_2$ and $Y_3$ because Y could always do better playing $Y_1$ or $Y_4.$ The new game is