This section lays out a useful way to reach a Nash Equilibrium of a game.

One strategy (strategy A) is said to "dominate" another strategy (strategy B) if a player is always better off choosing A instead of choosing B, regardless of the strategies chosen by other players.

To be a bit more precise, strategy A strictly dominates strategy B if the payoff for choosing strategy A is always strictly larger than the payoff for choosing strategy B. Strategy A weakly dominates strategy B if the payoff for choosing strategy A is always at least as large as the payoff for choosing strategy B.

A strategy is called a dominant strategy if it dominates all other strategies.

Dominant strategies should make it easy to predict the outcome of a game, but there can sometimes be complications even then. The Prisoner's Dilemma is a two-player game, where each player has a dominant strategy (Defect), but it is not uncommon for one or both players to chose the dominated strategy (Cooperate) instead.

Sometimes with more complex games, a pure strategy Nash equilibrium can be found (or at least the game can be simplified) by "iterated elimination of dominated strategies." The idea is to find a strategy which is dominated, and simply remove it from the game. (This can be done with either strictly dominated or weakly dominated strategies. However, eliminating weakly dominated strategies is riskier, and can cause the removal of Nash equilibria.) After removing that strategy, go looking for another strategy which is dominated, and remove it, etc. If you're lucky, this will whittle the game down to a single strategy per player. If you're not so lucky, you may at least find the game to be smaller and easier to cope with by other methods.

To look at an example click here