Dominated Strategy
What is Dominated Strategy?
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.
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.
Dominated Strategy: a worked example
A retailer picks Premium, Standard, or Budget while a rival picks Left or Right, with payoffs written as (retailer, rival). Against Left the three rows pay (5, 2), (4, 3) and (3, 1); against Right they pay (1, 4), (3, 1) and (0, 3). Budget loses to Standard in both columns, 3 against 4 under Left and 0 against 3 under Right, so Budget is strictly dominated and can be crossed off. The retailer still has no dominant strategy, since Premium wins under Left with 5 against 4 while Standard wins under Right with 3 against 1.
The mistake students make with dominated strategy
Students often cross off a strategy because it contains the lowest single payoff in the table, or because it does badly against the opponent's most likely move. Dominance is a stronger test than that: the strategy must lose against every one of the opponent's choices, checked one column at a time. The other frequent slip is treating dominated and dominant as the same word. A dominated strategy is one you would never play; a dominant strategy is one you would always play.
Dominated Strategy questions
What is the difference between a dominant and a dominated strategy?
A dominant strategy is your best move against every choice the opponent could make, while a dominated strategy is worse than one of your other moves against every choice. They are opposite ends of the same comparison. Rational players always play a dominant strategy and never play a strictly dominated one.
Can a game have a dominated strategy but no dominant strategy?
Yes, and it happens often once a player has three or more options. Ruling out one option as always worse than another says nothing about whether any single remaining option is best in every column. You cross off the dominated row and then solve the smaller game with best responses.
What does weakly dominated mean?
A strategy is weakly dominated when another strategy does at least as well against every opponent choice and strictly better against at least one. Strict dominance is the stronger version, where the other strategy wins in every column outright. Exam questions normally use strict dominance, because the order in which you eliminate weakly dominated strategies can change the answer.
Related terms
Common comparisons
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