Lesson preview · Game Theory Basics
Dominant Strategies
~5 min · Free to read
In the Prisoner’s Dilemma, Defect was the right move whatever the other player did. That’s a stronger property than just “best response to what I think the other is doing”. When a strategy wins regardless of the rival’s choice, it is called a dominant strategy. The player doesn’t need to predict anything — the same answer holds in every column.
Key Term
Dominant and dominated
- Dominant strategy — best response to every action the opponent could take.
- Dominated strategy — some other strategy always gives a higher payoff, regardless of what the opponent does. A rational player never plays a dominated strategy.
- Iterated elimination of dominated strategies (IEDS) — remove dominated strategies one player at a time. The reduced game is often simpler to solve.
The candidate strategy must beat (or tie) every alternative in every scenario.
Not every game has dominant strategies. When there is none, the player must think about which moves the rival is likely to make. When a dominant strategy does exist, the analysis collapses: play it. In the Prisoner’s Dilemma, Defect is dominant for both players. Most real oligopoly games are not that clean.
Worked Example
Firm A chooses Left or Right. Firm B chooses Up or Down. Payoffs (A, B): (L, U) = (3, 2); (L, D) = (4, 1); (R, U) = (1, 3); (R, D) = (2, 2). Does either firm have a dominant strategy?
Check yourself · no marks
If a player has a dominant strategy, should they always play it? What if the opponent has one too?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Practice · 1 / 4
A dominant strategy is one that:
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