Dominant Strategy vs Dominated Strategy
Dominant Strategy and Dominated Strategy are related concepts in AP Economics that students often mix up. A dominant strategy is a strategy that results in the highest payoff for a player regardless of the strategies chosen by other players. A dominated strategy is one that pays less than some other strategy of yours no matter what the opponent does, so a rational player never plays it. Here is how they compare side by side.
In game theory, a dominant strategy is the best course of action for a player in a game, no matter what the opponents do. If a player has a dominant strategy, they will always choose it. Not all games have a dominant strategy for each player.
Compare two of your own strategies column by column, holding the opponent's choice fixed each time. If one of them loses in every single column, it is strictly dominated and can be crossed off, because there is no belief about the opponent that would make it worth playing. Crossing off dominated strategies can shrink a large game until only one cell survives, a method called iterated elimination. Do not confuse this with a dominant strategy, which is the mirror image: a dominant strategy beats all of your other options against every opponent move. A game can contain dominated strategies while neither player has a dominant one, and a strategy that is merely bad in one column is not dominated at all.
Dominant vs Dominated Strategy: The Move That Always Wins and the One That Never Does
| Dominant Strategy | Dominated Strategy | |
|---|---|---|
| What it means | Pays more than every other strategy of yours, whatever the opponent does | Pays less than some other strategy of yours, whatever the opponent does |
| What a rational player does with it | Plays it every time | Never plays it |
| How many one player can have | At most one | Several at once, in a game with several strategies |
| Use when solving a game | Settles that player's move outright | Gets crossed off, shrinking the grid by a row or a column |
| In a prisoner's dilemma | Defecting is dominant for both players | Cooperating is dominated for both players |
| Link to Nash equilibrium | If both players have one, that pair is the only equilibrium | It never appears in any equilibrium of the game |
| The mistake to avoid | Calling a strategy dominant when it only wins against one of the opponent's moves | Crossing a strategy off when it only loses against one of the opponent's moves |
Both words compare two of your own moves, held across everything the opponent might do
Neither term describes a move that is simply good. Each describes a comparison between two of your own strategies that has to survive every column of the grid. Write payoffs as (row player, column player). Row picks Top or Bottom, Column picks Left or Right, and the four cells pay Top with Left (3, 3), Top with Right (1, 4), Bottom with Left (0, 1), Bottom with Right (2, 2). Check Column first, holding Row fixed. If Row plays Top, Column earns 3 from Left against 4 from Right, so Right wins. If Row plays Bottom, Column earns 1 from Left against 2 from Right, so Right wins again. Right is dominant for Column and Left is dominated. Now run Row. Against Left, Top pays 3 and Bottom pays 0, so Top is better. Against Right, Top pays 1 and Bottom pays 2, so Bottom is better. The comparison flips, so Row has neither a dominant nor a dominated strategy. That is the ordinary case rather than a trick. Plenty of games hand you one player whose move is settled by dominance and many hand you none, which is why /glossary/nash-equilibrium is the general solution concept and dominance is only a shortcut.
A Nash equilibrium can be built from strategies that are not dominant
Cross Left off the grid above, since Column will never play it, and one column is left standing. Row now compares Top, paying 1, against Bottom, paying 2, and takes Bottom. The pair Bottom with Right, paying (2, 2), is the prediction. Confirm it the way an equilibrium has to be confirmed, by testing one player at a time. Row switching to Top falls from 2 to 1, so Row stays put. Column switching to Left falls from 2 to 1, so Column stays put. Neither gains by moving alone, so this is an equilibrium, and it is the only one. Look at what Row is doing there. Bottom is not dominant, since Top beats it whenever Column plays Left. It is simply Row's best reply to the move Column will actually make. Two answers lose marks here. One says an equilibrium requires dominant strategies. The other says a game with no dominant strategy has no equilibrium. The cell paying (3, 3) makes the point from the other side, because both players prefer it to (2, 2), yet Column can lift its payoff from 3 to 4 by switching to Right, so it cannot hold.
Frequently asked questions
What is the difference between a dominant and a dominated strategy?
A dominant strategy beats every other option you have no matter what your opponent does, and a dominated strategy loses to some other option you have no matter what your opponent does. They are opposite verdicts from the same test, run across every move the opponent could make. If you hold a dominant strategy then all of your remaining strategies are dominated, but the reverse does not follow.
Can a player have two dominant strategies?
No, a player can have at most one, because a dominant strategy must beat every alternative, and two strategies cannot each beat the other. If two of your strategies pay exactly the same against every opponent move, neither one dominates, and the game has no dominant strategy for you. That tie is a common way for a question to look as though it has two answers when it has none.
Does every game have a dominant strategy?
No, and most do not, which is why exams give partial credit for spotting that dominance settles nothing in a particular grid. A coordination game has none, since each player's best move depends entirely on the other. Equilibrium survives the gap, because once players are allowed to randomize over their moves, every finite game has at least one.
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