In game theory, a dominant strategy is the one that gives a player the most benefit no matter what the other players do. Game theory is the branch of mathematics that analyzes strategies used in competitive situations in which the outcome of a player's actions depends on the actions of other players. In each game, there must be at least two players, and their choices can listed in a matrix that shows how each of their strategies affects the other. Dominant strategies are most often present in so-called zero-sum games, in which one player gains all only at the expense of the other. For example, if the prize for winning is a predetermined amount of money, the only way for one player to win all of it is for the other player to win none of it.

Strategies can be identified as strongly dominant or weakly dominant, depending on the difference between the most benefit that can be achieved and the least benefit — or no benefit. If the benefit of a dominant strategy yields only marginally better results, it is considered to be weakly dominant. Depending on the game, the dominant strategy is not always easy to identify, because of the various effects that other players' choices can have on different strategies.

When there is a dominant strategy, every other strategy is dominated. A dominated strategy is one that will always earn the player a smaller payoff, no matter what the other players do. It is possible for there to be dominated strategies without a dominant strategy, however.

Even when there are dominant strategies available, games can often end up in a tie. Such situations are covered and often predicted by the Nash Equilibrium, which exists when no player would make a different choice unless another player changed his or her strategy. When there is a Nash Equilibrium, however, players have no desire to change strategies because they would be worse off unless another player also changed strategies.