Looking for dominant strategies is a great way to find an equilibrium in many games. However, there are also a lot of games where this won€™t work because not all players have dominant strategies. If one player has a dominant strategy but the other doesn€™t, game theorists remove the first player€™s dominated strategies (the strategies that are always worse than some other strategy) and then continue to work toward solving the game with what€™s left. Let€™s take a look at an example of this. Consider the following payoff table, where the outcomes are written in the form {A€™s payoff, B€™s payoff}. Each player has four choices, which might make this game seem intimidating, but it€™s not.

Start off by trying to figure out whether any player has a strategy that is never best, and then eliminate it. The first one is done for you; no matter what move A makes, B€™s best response is never to play Red. Since B will never play Red, we don€™t even have to consider that as part of the game. Next, figure out if there€™s a move A will never make, then B, and so on. What is the equilibrium?

B's Strategies Red Ble reen Yellow Red (1, (2,7) (3,5 (4,6) Blue (2,2 (3,2 ,3 (4, 4) 2) Yellow4,(4,0)(5,0(5, 1) A's strategies Gre(3,2 (6,),3) B's Strategies Red Blue Green Yellow Red ft(2.7 (3.5 (4. 6) Blue 2,2 (3,2 (6, (4,4) Green3,2(6, (1,3) (3,2) Yellow| 1 (4,0) | (5,0) | (5,1) A's strategies