Open this lesson in your favourite AI. It'll walk you through the why, explain the demo, and quiz you on the try-it list.
If a strategy is worse than another no matter what anyone else does, a rational player never plays it. This is the closest thing to a free lunch in game theory — you can eliminate dominated strategies without any assumptions about what the other player believes. Dominant strategies, when they exist, are even cleaner: there is literally no argument about what to play. Getting fluent at spotting dominance, strict vs weak, is how you chop down a 10x10 game to something you can reason about.
Strategy is strictly dominated by if does strictly better than against every strategy profile of the others:
Use these three in order. Each builds on the one before.
In one paragraph, explain the difference between a dominant strategy and a dominated strategy in plain language.
Walk me through how I check whether a strategy is strictly dominated in an $n \times m$ game — what exactly do I compare? Where is it tempting to make mistakes?
Why is eliminating strictly dominated strategies considered 'safe' reasoning, while eliminating weakly dominated ones can change the set of predictions? Give a small example where the order of weak elimination matters.