9. Suppose Warner Music and Universal Music are in a duopoly and currently limit themselves to 10 new artists per year. One artist sells 2 million songs at $1.25 per song. However, each label is capable of signing 20 artists per year. If one label increases the number of artists to 20 and the other stays the same, the price per song drops to $0.75, and each artist sells 3 million songs. If both labels increase the number of artists to 20, the price per song drops to $0.30, and each artist sells 4 million songs. Explain how revenue payoffs for each scenario are calculated.If this game is played once, how many artists will each producer sign, and what will be the price of a song?If this game is played every year, how many artists will each producer sign, and what will be the price of a song? ### Game Theory in Music Industry CompetitionThe table above represents a simplified payoff matrix using game theory to analyze potential outcomes for two music companies, Warner Music and Universal Music Group, based on their strategic choices: either to "Collude" or "Compete."#### Matrix Explanation:- **Warner Music Options:** - **Collude** - **Compete**- **Universal Music Group Options:** - **Collude** - **Compete**#### Outcomes:1. **Both Collude:** - **Warner Music Revenue:** $25.0 million - **Universal Music Group Revenue:** $25.0 million2. **Warner Music Colludes, Universal Music Group Competes:** - **Warner Music Revenue:** $22.5 million - **Universal Music Group Revenue:** $45.0 million3. **Warner Music Competes, Universal Music Group Colludes:** - **Warner Music Revenue:** $45.0 million - **Universal Music Group Revenue:** $22.5 million4. **Both Compete:** - **Warner Music Revenue:** $24.0 million - **Universal Music Group Revenue:** $24.0 million### Analysis:The matrix illustrates potential financial outcomes depending on whether both companies choose to cooperate (collude) to maintain higher prices or compete aggressively. In this scenario, mutual collusion benefits both, but competitive tactics can yield greater individual profits if one company exploits the other's collusion.

The study of strategic interactions and mathematical models is done in game theory. A dominant strategy is a strategy that the player chooses irrespective of other players' actions. The best strategy in a non-cooperative game can be achieved through Nash equilibrium. Nash equilibrium is not always Pareto efficient.(1)Given that each label is capable of signing 20 artist but they sign only 10. In a case where both labels collude then their revenue will be equal to: Revenue= No of artist ×each artist total songs× Rate of songsRevenue= 10×2×1.25Revenue=$25 million In a case where one label signs 20 artist and other hires only 10 then the revenue (R') of label signing more artists will be : R'= No of artist ×each artist total songs× Rate of songsR'= 20×3×0.75R'=$45 million The revenue(R") of label signing only 10 artists will be ; R"= No of artist ×each artist total songs× Rate of songsR"= 10×3×0.75R"=$22.5 million If both labels increases the signed artist to 20 then their revenue(R*) will be ; R*= No of artist ×each artist total songs× Rate of songsR*= 20×4×0.3R*=$24 million Hence, when both labels collude their revenue will be($25 million, $25 million). When labels compete their revenue reduces to($24 million $24 million). When one compete and one collude, their revenue will be ($45 million, $22.5million) (2) If a game is played once then their best strategy will be : LABEL U COLLUDE COMPETE LABEL W COLLUDE $25m $25m $22.5m $45m COMPETE $45m $ 22.5m $24 m, $24m The best strategy is highlighted for each label if the game is played only once. The first one is the payoff of label W and the other one is of label U. If label W wants to collude then label U will compete because it will get a payoff of $45 m by doing that which is more than the payoff from colluding. Let's highlight the strategy. When label W competes, label U will compete. Similarly, label W will compete when label W colludes and competes.The highlighted portion is the Nash equilibrium. The Nash equilibrium can be verified by the fact that both labels will decide to compete irrespective of other players' actions. So, (compete, compete ) is a Nash equilibrium.Thus , when the game is played once, price of the song will be $0.3 and 20 artists will be signed by each label(3)When the game is played every year, then both labels cannot compete. Both labels will get $24 million by competing which is less than the revenue they can generate if they collude. So, (compete, compete) cannot be a possibility in a long run.(Collude, compete) or (compete, collude) are also not possible in long run. It is because if one label competes and gets more revenue in one year, then another label will also do the same thing in the next year. This will drag both labels to compete.Hence, both labels should collude and get a revenue of $25 m each year. They will sign 10 artists and the price of the song will be $1.25 per song.(1)When labels compete their revenue reduces to($24 million $24 million). When one colludes and competes their revenue will be ($22.5 million, $45million) and when both labels collude their revenue will be($25 million, $25 million).(2)The price of the song will be $0.3 and 20 artists will be signed by each label in a case where the game is played once.(3)The price of the song will be $1.25 and 10 artists will be signed by each label in a case where the game is played every year,