Iterated Dominance

The 4-step routine

1. Delete the opponent's strictly dominated strategies. Compare their payoffs across columns (or rows if they choose rows). If one option is worse for them in every scenario you can generate, a rational opponent will never play it — remove it from the matrix.
2. Re-check your own strategies in the smaller game. A strategy of yours that wasn't dominated before may become dominated now that some opponent options are gone. If so, eliminate it.
3. Repeat from both sides until stable. Keep removing dominated strategies — from either player — until the matrix shrinks no further.
4. What remains is your prediction. If a single cell survives, it is the outcome under common knowledge of rationality. If multiple cells remain, further analysis (best response, Nash) is needed — see Lesson 04.

Worked example — 2×3 matrix

You = rows {Up, Down}; Opponent = columns {Left, Middle, Right}. Cells = (your payoff, their payoff).

Elimination order:

1. Delete Right — Middle gives the opponent 2 (vs Right's 1) when you play Up; 1 (vs 0) when you play Down. Middle strictly dominates Right for the opponent.
2. Delete Down — In the {Left, Middle} sub-game, Up gives you 1 (vs Down's 0) against Left, and 1 (vs 0) against Middle. Up strictly dominates Down.
3. Opponent picks Middle — With only Up remaining for you, they compare Left (0) vs Middle (2). Middle wins.

Predicted outcome: (Up, Middle) = (1, 2). You earn 1; opponent earns 2.

Common knowledge of rationality

• IEDS assumes: everyone is rational, and everyone knows everyone knows that (and so on, infinitely).
• Valid when both parties are experienced and clear-headed.
• Use cautiously against erratic, first-time, or emotionally driven opponents.

Beauty contest — levels of thinking