Question

Consider two strategically dependent firms in an oligopolistic industry, Firm A and Firm B. Firm A knows that if it offers extended warranties on its products but Firm B does not, it will earn $\backslash (6$ million in profits, and Firm B will earn $\backslash )2$ million. Likewise, Firm B knows that if it offers extended warranties but Firm A does not, it will earn $\backslash (6$ million in profits, and Firm A will earn$\backslash )2$ million. The two firms know that if they both offer extended warranties on their products, each will earn $\backslash (3$ million in profits. Finally, the two firms know that if neither offers extended warranties, each will earn $\backslash )5$million in profits.

a. Set up a payoff matrix that fits the situation faced by these two firms.

b. What is the dominant strategy for each firm in this situation? Explain.

Short answer

(a) Profitability of firms A and B based on their respective strategies.

(b) Firm B has the biggest reward, regardless of Firm A's strategy.

Firm A and Firm B benefit from this arrangement because it ensures that each firm receives the highest possible reward.

Step-by-step solution

Given  information 

The profit that is earned will be $6 million in profits. by Firm A.

The profit that is earned will ne $2 million in profits by Firm B.

The profit earned by both the firms altogether is $3 million.

The profit earned by both the firms when none gave the warranty is $5 million.

Explanation 

• The two players in a particular game are Company A and Company B.
• Each player in this game has two strategic options.
• He or she knows or doesn't know the extended warranty.

Given information

The given sentences are: (a).

The following payoff matrix describes the given situation

Explanation (a)

a.

The variousresults of strategicdecisions aredisplayed inthe payment matrix. The payoff matrix isa way to explain game theory. The following payoff matrixshows a specific situation.

The profit of firms A and B based on their respective strategies is represented by the payoff matrix above. Firms A and B must each select the most profitable strategy.

Given information 

The given sentences are : (b).

If the firms successfully establish a cartel

Explanation (b)

b

A strategy is said to be dominant if it gives the player the best reward-to-risk ratio.

Regardless of what other players do, it is clearly the ideal reaction.

In the preceding game, regardless of Firm B's strategy, Knows' strategy guarantees Firm A the highest payoff.

Similarly, regardless of which strategy Firm A employs, the 'Knows' strategy ensures that Firm B receives the highest payoff.

Given information 

The given sentences are :

The strategy 'Knows' is the dominant strategy.

Explanation 

As a result, the 'Knows' method is the most popular among both Business A and Firm B, as it guarantees each firm the maximum potential payoff.