Question about strictly dominant/dominated strategies

Question

In this case, are there any strictly dominant or dominated strategies? matrix

My thought process: there is no strictly dominant/dominated strategy. Choosing 'M' is weakly dominated for the row player, but not strictly because it may yield the same payoff as another strategy (depending on what the opponent chooses). But it is not always a worse strategy (sometimes it's an equal strategy).

Is this correct? On the other hand, I could see it being strictly dominated because it will never give a higher payoff, so there's no reason to choose it and the opponent will always go with another one. But not sure.

Answer 1

Strategy $B$ strictly dominates $M$ for the row player assuming the payoffs are listed as (row player, column player).

Answer 2

As far as I understand, M is strictly dominated because row player would not choose it in any situation (If column player plays L, row chooses B. If column player plays C, row, chooses U. If column plays R, row chooses B).

The way to see this is to compare the expected benefit of each course of action for row player one column at the times. Then mark the best one for each situation. If you end up with a strategy (row) not choosen in any situation that means that it is strictlt dominated. Because it is not the best response in any posible scenario.

Cheers brother. Greatings from ARG.

Answer 3

Strict domination means that the pay off for the strictly dominated strategy is (strictly) lower than another strategy for all strategies of the opponent.

Choosing M will always yield a lower pay off than B. That’s why M is strictly dominated.

You’re right about the fact that you would never choose a strategy if the pay off from a strategy is at best equal to the pay off of another strategy. But that just not what strict domination means. It’s means always lower pay off.

Answer 4

I will try to answer this question:

Dominant A strategy is strictly (or strongly) dominant if it leads to better or the best outcomes than alternative strategies. A strategy is weakly dominant if it leads to equal or better outcomes than alternative strategies.

Dominated A strategy is strictly (or strongly) dominated if it leads to worse or the worst outcomes than alternative strategies. A strategy is weakly dominated if it leads to equal or worse outcomes than alternative strategies.