Dominated Strategy

A strategy $s_i$ is strictly dominated by $s_i'$ if, for every possible strategy of the opponent, $s_i'$ gives a strictly higher payoff:

A rational player will never play a strictly dominated strategy. Weak dominance is the same condition with $\geq$ everywhere and strict inequality in at least one case.

When to use

Check for dominated strategies as the first move when solving any Normal-Form Game. If a strategy is strictly dominated, eliminate it and recurse — this is Iterated Dominance (IESDS). Any Nash Equilibrium survives IESDS, so the procedure is a safe pre-filter before searching for NE. Don't confuse "dominated" with "not a best response": dominance must hold against every opponent strategy.