Question

Attaburger and Beefsteak are the only two fast-food hamburger restaurants in a small town. Each firm can choose to set a high price or a low price for a hamburger meal. The payoff matrix below shows the daily profits for any combination of strategies the two restaurants can choose. The payoff for Attaburger is listed first; the payoff for Beefsteak is listed second. Assume both restaurants have complete information. If Attaburger selects a high price, what strategy will Beefsteak select? Explain using the dollar values in the payoff matrix. Does Beefsteak have a dominant strategy? Explain using the dollar values in the payoff matrix. Assume that Attaburger and Beefsteak collude, both agreeing to choose high prices in order to maximize their joint profit at $23. If such an agreement is not legally enforceable, does Attaburger have an incentive to break the agreement? Explain using specific values. Instead of colluding, the firms simultaneously select their prices. In the Nash equilibrium, what are the daily profits for each of the following? Attaburger Beefsteak

Answer 1

Answer:

Task a: Explanations are shown below

Task b: Explanations are shown below

Task c: Explanations are shown below

Task d: Explanations are shown below

Explanation:

Task a:

If Attaburger selects a high price, what strategy will Beefsteak select?

Solution:

If Attaburger selects high price, beefsteak will get more profit from low price ($14), as $14 is greater than $13. Beaf stake will select low price. Pay-off values represent profits to restaurants.

Task b:

Does Beefsteak have a dominant strategy? Explain using the dollar values in the payoff matrix.

Solution:

When Attaburger chooses high price, Beefsteak's best response is low price ($14).

When Attaburger chooses low price, Beefsteaks's best response is high price $8.

therefore, there is no dominant strategy for beefsteak, as there is no strategy which is always its best response.

Task c:

Assume that Attaburger and Beefsteak collude, both agreeing to choose high prices in order to maximize their joint profit at $23. If such an agreement is not legally enforceable, does Attaburger have an incentive to break the agreement? Explain using specific values.

Solution:

Both choose high price = ($10 and $13)

so that their joint profit is $23 ($10 + $13)

Yes, Attaburger has an incentive to break the agreement. This is because his profit by choosing high price is $10, but he can get higher profit $12 by charging low price when beefsteak is charging high price. Therefore, Attaburger's profit would increase to $12, whereas, Beefsteak's profit would decrease to $8 - ($12, $8).

Task d:

Instead of colluding, the firms simultaneously select their prices. In the Nash equilibrium, what are the daily profits for each of the following?

1. Attaburger

2. Beefsteak

Solution:

From part b, we know best responses of beefsteak.

Now we need to look at the best response of Attaburger.

• When beefsteak chooses high price, Attaburger's best response is low price - $12.
• When beefsteak chooses low price, Attaburger's best response is low price - $9.
• Thus we observe, that best response of both restaurants occur simultaneously when Attaburger chooses low price ($12), and beefsteak chooses high price ($8). Thus equilibrium is ($12, $8).

(i) Attaburger's profit is $12

(ii) Beefsteak profit is $8