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Cooperative and non-cooperative outcome

Question:

Cineplex and AMC are two rival movie theatre chains. They must each decide whether to set an admission price of $10 or set an admission price of $12; of course, the number of movie goers (and thus their revenues) will depend both on the price they set as well as the price charged by their competitor. Their profit levels are given in the matrix below.

 

Cineplex

$10

$12

 

AMC

$10

(7,7)

(8*,8*)

$12

(6,8)

(7,7)

a) If AMC and Cineplex could cooperate, which set of actions would generate the highest industry profit? Is that outcome likely to be achievable?

Answer:

If both firms cooperate, then AMC will charge $10 and Cineplex will charge $12. This maximizes there and also the industry profits. Also, this is the most likely outcome in the market as for AMC charging $10 is the dominant strategy, regardless of what Cineplex charges. Given this strategy of AMC, charging $12 is the best strategy for Cineplex.

b) What is AMC's best action(s)? Does it depend on Cineplex's action?

Answer:

As discussed above, AMC's best action is to charge $10, regardless of what Cineplex charges. Therefore, this is also AMC's dominant strategy.

c) What is Cineplex's best action(s)? Does it depend on AMC's move?

Answer:

If AMC charges $10, then Cineplex's best action is to charge $12 as it maximizes its profits. If AMC charges $12, then Cineplex's best strategy is to charge $10, as it maximizes its profits. As we see, Cineplex's best actions are dependent upon AMC's moves.

d) If Cineplex and AMC cannot cooperate, what outcome(s) would occur? Is there a difference between the cooperative and non-cooperative outcome?

Answer:

The Nash equilibrium in this game is the same as the cooperative and non-cooperative outcome , i.e., AMC charges $10 and Cineplex charges $12. This is because of the fact that this optimizes both firms' profits.

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