Iterated dominance
Also known as: Iterated elimination of dominated strategies
Solve a game by repeatedly deleting moves no rational player would make.
What it means
A solution procedure that removes strictly dominated strategies one round at a time: once obviously bad options are deleted for one player, new options may become dominated for another, and the process repeats. If it leaves a single strategy per player, the game is said to be dominance solvable. The method assumes not just rationality but common knowledge of rationality — each player must trust that others will also delete, and trust that others trust this, and so on. It matters because it links rationality to higher-order beliefs, and behavioral experiments like the beauty-contest game show people perform only a few rounds of such reasoning.
Examples
In a guessing game, no one should pick above the rational ceiling, and knowing that lowers the ceiling again, round after round.
Two rival shops on the same street know neither would ever price above the other, so each shaves a penny; anticipating the other's shaving pushes both prices down toward cost.
Haggling over a flat, the buyer discards offers the seller would certainly refuse; the seller, expecting exactly that, discards asking prices the buyer would walk away from. Each round narrows the range.
First described in Game theory; refined by Bernheim & Pearce (1984).