2. (a) Firm 1 does not have a dominant strategy, its best response depends on what firm 2 does. Firm 2 however does have a dominant strategy, it will always be best for 2 to charge the low price whatever firm 1 does. Firm 2 will never charge the high price and firm 1 knows this. This means that we can delete the column where 2 play high from consideration, reduce the game to the following payoff matrix.

Once we have reduced the game by removing 2's dominated strategy (a strategy that is never used), it is clear that in this reduced game it is dominant for 1 to play low as well, leading to both firms playing low as shown below:



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