Iterated Dominance

Iterated Elimination of Strictly Dominated Strategies (IESDS) is the procedure of successively removing strictly dominated strategies from a game and repeating on the reduced game until none remain. Rational players never play a dominated strategy, and they know their opponents are rational too — so eliminating dominated rows/columns is safe. The order of elimination does not affect the final result, and a Nash Equilibrium is never eliminated by IESDS: if IESDS yields a unique outcome, that outcome is the unique NE.

When to use

Run IESDS as a pre-filter on any Normal-Form Game before searching for Nash Equilibria — it shrinks the matrix and often pinpoints the equilibrium directly. The same logic, applied to a continuous strategy space with no other equilibrium refinement, drives the Traveller's Dilemma unravelling. State explicitly whether you are using strict or weak dominance — the exam may specify, and strict is the safer default.