Strictly dominated strategies game theory

In order to achieve better outcomes than strategies B and C, strategy A is dominant. In the case of strategy A and strategy B, both lead to equal outcomes, but both lead to better outcomes than strategy C, then strategy C is dominated, and you should avoid it.

No matter how other players behave, the dominant strategy is the best option for an individual in a game. Can There Be 2 Dominant Strategies? Watch how to determine dominant strategy in game theory microeconomics Video. Around The Web. In the first step, at most one dominated strategy is removed from the strategy space of each of the players since no rational player would ever play these strategies.

This results in a new, smaller game. Some strategies—that were not dominated before—may be dominated in the smaller game. The first step is repeated, creating a new even smaller game, and so on. The process stops when no dominated strategy is found for any player. We use the same methodology to examine whether Player 2 has a strategy that is always best, for every possible choice of Player 1.

If we think that Player 1 will choose A , Player 2 earns more from V a payoff of 9 than from W a payoff of 1 or X a payoff of 6. If we think that Player 1 will choose B , Player 2 earns more from X a payoff of 9 than from V a payoff of 8 or W a payoff of 2. Since Player 2 does not have a single strategy that is always best sometimes Player 2 prefers V and sometimes Player 2 prefers X , Player 2 does not have a dominant strategy.

A Dominated Strategy is a strategy that is always worse than some other strategy no matter what other players do. While Player 2 does not have a dominant strategy in the game above there is no one strategy that is always best , Player 2 does have a strategy that doesn't seem very useful. Consider the strategy W. Note that W is always worse than V. No matter what Player 1 does plays A or B , Player 2 's strategy of W always earns less than Player 2 's strategy of V 7 is worse than 9 and 2 is worse than 8.

We say that strategy W is dominated by V or, more simply, that strategy W is dominated. Note that when a player has a dominant strategy, all of that player's other strategies must be dominated by that dominant strategy.

However, a player can have a dominated strategy without having a dominant strategy like Player 2 in the example above. To understand this dictinction, consider the following mathematical facts. If we can say that a player's strategy earns at least as much as weakly more, i.