Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs:
Firm B - low output Firm B - high output
Firm A - low output 300, 250 200, 100
Firm A - high output 200, 75 75, 100
1. What are the dominant strategies in this game?
A. Both firms produce low levels of output.
B. Firm A's dominant strategy is to produce low levels of output, but Firm B does not have a dominant strategy.
C. Firm B's dominant strategy is to produce low levels of output, but Firm A does not have a dominant strategy.
D. Both firms produce high levels of output.
E. Neither firm has a dominant strategy.

Game theory involves two players. They have more than one option to decide. Pay off from each options adopted by two players are available. They have to select a strategy which will maximize their own return. But for optimizing their decision, they have to consider the action of his rival.

In this problem, two players are firm A and firm B. They have two strategies low output and high output. The strategies of firm a are measured in rows and for firm B in columns. They have to select a strategy which will maximize their payy off. Each cell has two pay offs. First one is for Firm A and second one is for firm B.

1. Dominant strategy is a strategy which will always give higher payoffs in comparison with pay off of other strategies. Consider first strategy of firm 1. If it adopts strategy of low output, then firm 2 can also adopt either strategy of low output or high output. In that case pay off of firm 1 will be 300 or 200.

Alteratively if firm 1 adopts high output then pay offs are 200 or 75. 200 is earned if firm B also go for low productivity. It is 75 if firm B adopts high productivity.

Now compare two payoffs side by side. Note that firm A has higher pay off in low output [300,200] in comparison with the pay off of high output [200,75]. So whatever strategy firm B adopts, Firm A will always go for low production. So low production strategy of firm A dominates high production strategy.

Same result is not observed for firm B. Pay off from low production strategy of firm B is [ 250,75]. Pay off from high production strategy are [100,100]. Now compare the two. If Firm A go for low production, then firm B will select low production. It will give pay off 250. Similarly when firm A decides for high production, then firm will also decide for high production. It will maximize its pay off. Amount is 100. Thus no strategy dominates for firm B.