Comparison
Nash equilibrium vs dominant strategy
One describes a single player's best move; the other describes the whole game sitting in a stable configuration.
A dominant strategy is one player's best move regardless of others' choices; a Nash equilibrium is a strategy profile where every player is best-responding to the others—so every dominant-strategy equilibrium is a Nash equilibrium, but not the reverse.
| Nash equilibrium | Dominant strategy | |
|---|---|---|
| Core idea | A strategy profile where no player can gain by unilaterally deviating. | A single action that beats every alternative no matter what rivals do. |
| Unit of analysis | The whole configuration—all players' choices at once. | One player's choice, considered in isolation. |
| Depends on others' moves | Yes—each move must be a best response to the others' actual moves. | No—optimal against every possible combination of others' moves. |
| Existence | Always exists (possibly in mixed strategies; Nash's theorem). | Often none—many games give no player a move that dominates. |
| Relationship | Broader concept; contains dominant-strategy equilibria as a special case. | Special case: if every player has one, all playing it is automatically a Nash equilibrium—but most Nash equilibria use no dominant strategy. |
| Typical example | Coordination game—two stable equilibria, no dominant move for anyone. | Prisoner's dilemma—'defect' dominates for each player individually. |
Bottom line
Reach for dominant strategy when you are analyzing one player and asking 'is there a move I should make no matter what?' Reach for Nash equilibrium when you want to predict the stable outcome of the whole game—the configuration nobody wants to walk away from.
The relationship is containment. If every player has a dominant strategy, everyone playing it is a Nash equilibrium—the 'dominant-strategy equilibrium,' the strongest and most robust kind, because the choice holds against every rival move. But the converse fails: most Nash equilibria, like the two corners of a coordination game, involve no dominant strategy at all; each move is only best given what the others actually chose.
So a dominant strategy is a property of one player's option; a Nash equilibrium is a property of the entire configuration. Every dominant-strategy equilibrium is Nash. Most Nash equilibria are not built from dominant strategies.
Full pages: Nash equilibrium · Dominant strategy
FAQ
Is a Nash equilibrium the same as a dominant strategy?
No. A dominant strategy is one player's best move regardless of what others do; a Nash equilibrium is a full strategy profile where each player is best-responding to the others. They coincide only in the special case where everyone's equilibrium move also happens to be dominant.
Is every dominant-strategy equilibrium a Nash equilibrium?
Yes. If each player plays a dominant strategy, no one can gain by deviating—exactly the definition of Nash. Dominant-strategy equilibria are a strict subset: the most robust Nash equilibria, since each choice holds against every rival move, not just the equilibrium one.
Does every Nash equilibrium have a dominant strategy?
No, and most don't. Coordination games, battle of the sexes, and every mixed-strategy equilibrium have Nash outcomes with zero dominant strategies—each player's move is only best given the others' actual choices, not best regardless of what they do.
What's the difference between Nash equilibrium and dominant strategy?
Scope. Dominant strategy is about one player: a move that beats all alternatives no matter what others do. Nash equilibrium is about the whole game: a strategy profile where every player is simultaneously best-responding, so no one wants to unilaterally switch.
Can a game have a dominant strategy but no Nash equilibrium?
No. Every finite game has at least one Nash equilibrium once mixed strategies are allowed (Nash's theorem), and a dominant strategy only reinforces that existence—it never destroys it. The real gap runs the other way: a game can have Nash equilibria yet no dominant strategy for anyone.
Related concepts
- Prisoner's dilemma — The canonical game where 'defect' is a dominant strategy and mutual defection is the resulting Nash equilibrium.
- Schelling point — A coordination outcome that is a Nash equilibrium with no dominant strategy—players match on focal points, not dominant moves.
- Tragedy of the commons — Each player's dominant strategy to overuse produces a Nash equilibrium that is collectively ruinous.
- Tit-for-tat — In repeated play, a strategy that isn't dominant yet can sustain cooperative Nash equilibria.