Game Theory

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  • Topic: Game theory, Film, Nash equilibrium
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  • Published : February 28, 2013
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Topic 5: Game Theory Applied to the Movie and Aviation Industries I. Case study: Game Theory Applied to the Movie Business
In the movie business, one of the trickiest decisions producers face is what type of movie to make. Suppose there are 2 movie studios and that their producers are trying to decide whether to make an Action Adventure (AA) or Romantic Comedy (RC) movie. Suppose each of the studios does not know what type of movie the competing studio is planning to make that same year and that they do not trust each other in the least. They face the following payoff matrix.

Studio 1
RC AA
Studio 2RC(50,50)(90,60)

AA(60,90)(75,75)

(Figures show total estimated box office revenues in $ millions for Studio 1, Studio 2.)

What strategy (make an AA or RC movie) should each of the studios chose? What is the payoff to each of the 2 studios given the strategies they choose?

Answer:
From Studio 1’s perspective:
Studio 1’s payoff

RC50

RC

AA90
Firm 2

RC60
AA

AA75
Same result from Studio 2’s perspective.

From studio 1’ s perspective: if studio 2 makes a RC, studio 1’s payoff is $50 million if it also makes a RC and $90 million if it makes an AA. If studio 2 makes an AA movie, studio 1’s payoff is $60 million if it makes a RC and $75 million if it makes an AA. Therefore, studio 1 will choose the strategy “make an AA movie”. Since the payoff matrix is symmetric (same payoffs to the studios for the same decisions) the same will apply to studio 2 will also choose the strategy “make an AA movie”. The resulting payoff will be $75 million for each studio.

Now, suppose that AA movies are much more expensive to make than RC movies and therefore the expected profitability of the two types of movies differ. Suppose that an AA movie costs $70 million per movie and a RC movie costs $25 million per movie. What strategy will each of the 2 studios choose?

What is the payoff to each of the 2 studios given the strategies they choose?

Answer:
New payoff matrix:
Studio 1
RC AA
Studio 2RC(25,25)(20,35)

AA(35,20)(5,5)

The new payoff matrix is derived by simply subtracting the cost of making the types of movies from the expected box office revenues. So, subtract $70 million (cost of making an AA movie) from box office revenues for AA and $25 million (cost of making a RC) from box office revenues for RC. For example, from the payoff matrix in part a: if studio 1 makes an AA movie and studio 2 makes a RC, the payoffs are $90 million to studio 1 and $60 million for studio 2. From these payoffs subtract $70 million for studio 1 and $25 million for studio 2. That gives the new payoffs of $20 million for studio 1 and $35 million for studio 2, as shown in the new payoff matrix.

New representation of the game:

From Studio 1’s perspective:
Studio 1’s payoff

RC25

RC

AA20
Firm 2

RC35

AA

AA5
From studio 1’s perspective, if studio 2 chooses to make a RC then studio 1’s payoff is $25 million if it also makes a RC and $20 million if it makes an AA movie. If studio 2 makes an AA movie, then studio 1’s payoff is $35 million if it makes a RC and $5 million if it makes an AA. Therefore, the dominant strategy for Studio 1 is RC. The outcome of the game is exactly the same from Studio 2’s perspective. So the dominant strategy for Studio 2 is also RC. The resulting payoff for the 2 studios will be $25 million each.

II. Case study: Game Theory Applied to the Aviation Industry Consider the international market for commercial aircraft. The development and production of new lines of aircraft are subject to significant economies of scale. Therefore, it does not pay to develop a new...
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