# Application of Nash Equilibrium and Game Theory with examples

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?

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

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

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

Summary:

This assignment in economics focuses on Nash equilibrium or game theory, introduced by Prof. John Nash. A case study involving game theory in deciding dominant strategy for two competing multiplexes is given and is solved in a step by step manner.

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