In the first game, Firm A goes first and then Firm B responds. Both firms know the payout matrix. Since the firms are rational they want to get their highest possible payout. They care about the absolute value of what they get, not about the comparison between what they make and what their competitor makes.
In that case, Firm A will produce a large amount. Firm B will then choose to produce a small amount because that will give it an output of 800 rather than 500 or 0. So Firm A will make 1400 and Firm B will make 800. So, who has the advantage here? And is their combined output of 2200 the best possible outcome or could they have made more if they made different choices?
In the second game, Firm A goes, then Firm B, then Firm A gets to go again. This should not cause any change in the outcome. Firm A will choose to produce a large amount. Firm B will still choose a small amount because if it chooses a large amount, it will only get 500. Firm A will not change.
The third game is different. The two firms have to go simultaneously and neither knows what the other will do. This is, essentially, a prisoners’ dilemma. Both firms will choose to produce a large amount because they do not want to pick small only to have the other firm pick large. Now, both firms get only 500 of output.