3) Consider the following game between Sony, a manufacturer of video cassette pl

Question

3) Consider the following game between Sony, a manufacturer of video cassette players, and Columbia Pictures, a movie studio. Each firm must decide whether to use the VHS or Beta format - Sony to make video players, Columbia to release its movies for rental or purchase.


Columbia Pictures
Beta VHS
Sony Beta 20, 10 0, 0
VHS 0, 0 10, 20

a) Restrict attention to pure strategies. Does either firm have a dominant strategy? What is (are) the Nash equilibrium (equilibria) of this game?
b) Is there a mixed strategy Nash equilibrium in this game? If so, what is it?

Explanation / Answer

This is a penny matching game. A. Sony has no dominant stategy. If Columbia picks beta, Sony should pick beta and if Columbia picks VHS, Sony should pick VHS. The same is true for Columbia. They are both better off if they pick the same format. There are two pure strategy Nash equilibria. Either they both pick Beta or they both pick VHS. B. There has to be a mixed strategy because there is always an odd number of Nash equilibria. Let's find it. let's assign p1 as the probability that Columbia chooses VHS and (1-p1) as the probability that it picks beta. Now, let's calculate Sony's expected utility from its choices. U(Beta) = 20p1 U(VHS) = 10(1-p1) In equilibrium, these are equal. 20p1 = 10(1-p1) 20p1 = 10 - 10p1 30p1 = 10 p1 = 1/3 So, Sony plays a mixed strategy of (Beta, Sony) = (1/3,2/3) Because this is a symmetric game, we can tell that Columbia will have the same thing but flipped. But you can do the math if you like. For Columbia, (Beta, Sony) = (2/3,1/3)

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