Dominant Strategy

A strategy that yields at least as high a payoff as any alternative regardless of others' play.

Ask the Game theory assistant1 min read · Updated September 9, 2026

Definition

$s_i$ strictly dominates $s_i'$ if $u_i(s_i,s_{-i})>u_i(s_i',s_{-i})$ for all $s_{-i}\in S_{-i}$ ; weak dominance replaces $>$ with $\ge$ (strict for some $s_{-i}$ ).

A strategy is (strictly) dominant if it (strictly) dominates every other strategy in $S_i$ .

Intuition

It's the best choice for player $i$ no matter what the opponents do — there is no scenario in which switching is better.

A dominant strategy makes strategic reasoning unnecessary: you should play it unconditionally.

Worked example

In the Prisoner's Dilemma, Defect strictly dominates Cooperate.

In a second-price (Vickrey) auction, truthfully bidding your value is a weakly dominant strategy.

The math

If every player has a strictly dominant strategy, the resulting profile is the unique Nash equilibrium (a dominant-strategy equilibrium).

Iterated elimination of strictly dominated strategies never removes a Nash equilibrium and commutes with order.

Where it is used

Dominant-strategy incentive compatibility (DSIC) is the gold standard in mechanism design — see VCG mechanisms.

Used to simplify analysis of auctions, voting rules, and contract design.

More in Game theory

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