Iterated Elimination of Dominated Strategies, explained.
Iterated strict dominance removes a strategy when another available strategy gives its player a higher payoff against every remaining opponent action.
Why it happens
A declared three-by-three payoff matrix is reduced through player-selected row and column removals. Invalid removals leave the strategy in place and explain the missing condition; the strict-dominance survivor is A,L.
Iterated strict dominance removes a strategy when another available strategy gives its player a higher payoff against every remaining opponent action.
Read the result
A removable strategy must lose strictly to some other active strategy at every active opponent action. A single favourable comparison is insufficient.
A worked example
Reduce a payoff matrix using valid eliminations
Remove row B after verifying that row A beats it at all three columns.
Remove column M and column R when the column player’s strictly better remaining alternative is checked across active rows.
With only L left, remove row C and inspect the surviving A,L profile.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A declared three-by-three payoff matrix is reduced through player-selected row and column removals. Invalid removals leave the strategy in place and explain the missing condition; the strict-dominance survivor is A,L.
Where this idea is useful
A practical use
Check every relevant opponent response before calling an option strategically inferior.
A common misconception
“A strategy is dominated if it loses in one cell.”
Strict dominance compares an alternative against every currently possible opponent response, so one bad outcome does not establish removal.
What this explanation leaves out
- Only pure strict dominance is used. Weak dominance, mixed domination, uncertainty about payoffs and beliefs require additional analysis.
Would the same rule safely remove all weakly dominated strategies?
Weak dominance has additional order and interpretation subtleties. This activity deliberately uses only strict payoff inequalities.
Have you checked the opponent response that makes your preferred elimination fail?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.