Suppose TimberPond and JayB are the only two music labels (i.e. companies) aroun

Question

Suppose TimberPond and JayB are the only two music labels (i.e. companies) around. Each of them currently limits the number of new artists per year to 10. Each of their artist sells 200 songs at $10/song. Each label is capable of signing 20 artists per year. If one label increases the number of artists to 20 and the other doesn't; the price of song drops to $3.50/song and each artist sells 300 songs. If both labels increase the number of artists to 20, the price per song drops to $2.00 and each artist sells 400 songs. Based on this information, answer the following questions: First of all, create a 2 Times 2 matrix showing the options (strategics) available to each label. Calculate their revenues (payoffs) under each situation If this game is played only ONCE, what will be the outcome? What will be the price of song? If this game is repeated every year for long enough time in the future, what will be the outcome? What will be the price of a song?

Explanation / Answer

Ans a) The strategies/options available to TimberPond and JayB are as follows:

Ans b) When each label chooses 10 artists, then each artists will sell 200 songs at $10/song. This implies total number of songs sold by each label is (10 * 200) = 2,000. This generates a total revenue of (2,000 * $10)= $20,000 for each label.

When one of the label hires 20 artists and the other label keeps the number of artist to 10, then each artist sells 300 songs at $3.50/song. Hence,

the label which increased the number of artists to 20 will sell a total of (300 * 20) songs = 6,000 songs which generates total revenue of (6,000 * $ 3.50) = $ 21,000

and the label which have kept the number of artists to 10 will sell a total of (300 * 10) songs = 3,000 songs which generates total revenue of (3,000 * $ 3.50) = $ 10,500

When both the labels increases the number of artist to 20, then each artist will sell 400 songs at $2/song which means each label will sell a total of (400 * 20) songs = 8,000 songs which generates a total revenue of (8,000 * $2) = $16,000 for each of the label.

Ans c) The payoff matrix is given below:

Each label has a dominant strategy of choosing 20 artists.

Hence, the Nash Equilibrium of this game is (20 artists, 20 artists) if the gae is played once. At this strategy the price of the song will be $2/ song.

Ans d) There is a proposition in game theory which says: When a game is played repeated stages, then if the stage game G has a unique Nash Equilibrium then, for any stage T, the repeated game G(T) has a unique subgame perfect oucome: The Nash Equilibrium of G is played in every stage.

Therefore, according to above proposition, the outcome of the above game when played repeatedly is 20 artists by each label and the price of a song is $2/ song.

TimberPond JayB Choose 10 artists Choose 10 artists Choose 20 artists Choose 20 artists

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