Question

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.

Answer 1

Answer:

Consider the following explanation

Explanation:

Context

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.