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I have a question about dominated strategy. I understand that dominated strategy is one which is dominated by another strategy. For instance if we have strategy L and H for a single player and if all payoffs of L are lower than that of H then we say L is "dominated" by H.

What if we have a situation where two of L's strategies are lower than that of H's but one of them is the same? e.g. $$L: 10, 2, 0 $$ $$H: 10, 5, 2, $$

We can see that $5>2$ and $2>0$ but $10=10$.

In this case, do we say that L is dominated by H? Or all payoffs need to be strictly greater for it to be considered dominated?

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There are strictly dominated strategies and weakly dominated strategies.

Strictly dominated strategies have payoffs always lower (i.e. "$<$") than another strategy that dominates it.

Weakly dominated strategies have payoffs always no higher (i.e. "$\le$") than another strategy that dominates it.

You example features $L$ as a weakly (not strictly) dominated strategy.

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