Iterated Elimination of Dominated Strategies
You can often solve a game without ever computing an equilibrium directly — just repeatedly cross out any move that's never your best choice, no matter what the opponent does, until only sensible moves are left.
Prerequisites: Game Theory Basics
Some games can be solved without ever building an equilibrium concept from scratch — you just need to notice that certain moves are simply bad, in a very specific sense: not bad on average, but bad no matter what the opponent does. Cross those out, and often the game shrinks enough that a second move becomes bad in the smaller game that's left, even though it wasn't bad in the original. Repeat until nothing more can be crossed out.
What "dominated" means precisely
A strategy is strictly dominated if some other strategy gives you a strictly better payoff against every single one of the opponent's possible choices — not on average, but in every column of the payoff table simultaneously. A rational player never plays a strictly dominated strategy, because there's a strategy that's unambiguously better regardless of what happens. Critically, once you've established the opponent would never play their dominated strategy either, you can delete that row or column from the table and look for new dominance in the smaller remaining game — a strategy that wasn't dominated originally can become dominated once you've correctly assumed the opponent won't play their own bad options.
Worked example
Two players choose simultaneously from {A, B, C}. Payoffs are (row, column):
| Col: A | Col: B | Col: C | |
|---|---|---|---|
| Row: A | (3, 3) | (0, 5) | (1, 4) |
| Row: B | (5, 0) | (1, 1) | (0, 2) |
| Row: C | (4, 1) | (2, 0) | (2, 2) |
Check the row player's options against each column: Row A gives (3, 0, 1) across the three columns, Row B gives (5, 1, 0), Row C gives (4, 2, 2). Row C beats Row A in every column (4>3, 2>0, 2>1) — Row A is strictly dominated by Row C and gets deleted. With Row A gone, check the column player in the remaining table (Rows B, C only): Column A gives the column player (0, 1), Column B gives (1, 0), Column C gives (2, 2). Column C beats both Column A and Column B in every remaining row — Columns A and B are dominated by C and get deleted. Now only Row B vs Row C remain, against the single remaining Column C: Row B pays 0, Row C pays 2 — Row B is now dominated (it wasn't dominated in the original full table, only after Column A and B were removed) and gets deleted. What's left: Row C, Column C, payoff (2, 2) — the unique outcome survives the full elimination process.
What this means in practice
Interviewers use small payoff-table games precisely because iterated dominance is a mechanical, checkable procedure — you don't need to guess an equilibrium, you just repeatedly ask "is there a row (or column) that's beaten everywhere by another?" and delete it. On a desk, this is the same discipline as ruling out strategies (aggressive quoting into a clearly better-informed counterparty, say) that are dominated regardless of what the counterparty does, before spending any effort optimizing among what's left.
Strict dominance means one option beats another against every possible opponent response, not just on average — and eliminating dominated strategies can be repeated, since removing an opponent's bad options can make a previously-fine strategy dominated in the smaller game that remains.
Don't confuse strict dominance (better in every column, always eliminate) with a strategy that's merely better on average or usually. A strategy that's fantastic against most opponent moves but catastrophic against one specific move is not dominated and cannot be safely deleted — the whole method only works because strict dominance requires unanimity across every column.
Related concepts
Practice in interviews
Further reading
- Osborne, An Introduction to Game Theory, ch. 2, 4
- Gibbons, Robert, Game Theory for Applied Economists, ch. 1