Game theory

Iterated Elimination of Dominated Strategies

Iteratively removing strategies that are strictly dominated.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

Let Si0=SiS_i^0=S_i and Sik+1={si∈Sik:∄si′∈Sik s.t. si′ strictly dominates si on S−ik}S_i^{k+1}=\{s_i\in S_i^k:\nexists s_i'\in S_i^k\text{ s.t.\ } s_i'\text{ strictly dominates } s_i\text{ on }S_{-i}^k\}; iterate.

A game is dominance-solvable if this process leaves a unique strategy profile.

Intuition

Common knowledge of rationality lets us remove strictly dominated options round after round.

Predicts behavior when players reason about what rational opponents would never do.

Worked example

The Keynesian beauty contest / "p-guessing" game is dominance-solvable with unique outcome 00.

Iterative dominance solves the traveler's dilemma at the minimum allowable value.

The math

Iterated strict dominance preserves all Nash equilibria and yields a unique outcome independent of the order of elimination.

Iterated weak dominance depends on the order and can discard Nash equilibria.

Where it is used

Solution tool in auction theory and contract design; conceptual underpinning of rationalizability.

Foundation for level-kk models of strategic thinking.

Go deeper

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