In game theory, a dominant strategy is the best strategy a player can use, regardless of what any other player does. A weakly dominant strategy is one such that the player can't do any better. A strongly dominant strategy is one where any other strategy will be strictly worse.

Nash equilibria in dominant strategies are generally better predictors of how games will turn out than other equilibria.

One way to solve for the Nash equilibrium of a game in strategic form is through "iterated elimination of strictly dominated strategies". It doesn't work for all games, but the idea is this:

  1. Find a strongly / strictly dominated strategy, any one, for any player.
  2. Kill that strategy. Cross it out.
  3. Now, rebuild the game with that strategy missing as an option.
  4. Go to step (1).
When you can't do any more, if you're lucky each player has only one strategy left, and you've found the Nash equilibrium. Even if you're not so lucky, you may have simplified the game so that it's easier to solve for Nash equilibrium using other techniques.

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