Suppose there are two sound recording companies, each of which has two possible actions to set...

  

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Suppose there are two sound recording companies, each of which has two possible actions to set either a 'low price' or 'high price'. Where both firms choose 'low price' this can be thought of as the competitive outcome, and where both firms choose 'high price' this can be thought of as the collusive outcome. Payoffs (profits) are as follows: Warner Low price High price Sony Low price 0,0 -10,60 High price 60,-10 50,50 a) Suppose the two sound recording companies interact once in the market and must choose their strategies simultaneously. Identify the Nash equilibrium of the game and explain why this is the Nash equilibrium. (3 marks) b) Suppose the two sound recording companies interact once in the market and choose their strategies sequentially. Warner chooses its strategy first, and Sony chooses its strategies second. (i) Draw the game tree that represents this game. (ii) What is the rollback equilibrium of the game? (4 marks) c) Suppose that the two sound recording companies interact once in the market. Suppose that, in the sequential version of the game, Sony has the opportunity to choose whether to advertise its product prior to both of the sound recording companies making their choices of prices. (That is, Sony chooses whether to advertise, then Warner chooses its price strategy, and then Sony chooses its price strategy.) If Sony does advertise then it incurs a cost of 10. The benefit of advertising is that it raises the payoff to Sony by 20 when both Sony and Warner choose 'High price'. (i) Draw the game tree that represents this game. (ii) What is the rollback equilibrium of the game? (4 marks) d) Suppose that the two sound recording companies interact indefinitely in the market. In each time period in which they interact, they choose their strategies simultaneously. (i) Suggest a strategy that the sound recording firms might adopt to sustain the collusive outcome as a Nash equilibrium. (ii) Give some intuition for why your suggested strategy for each firm will allow the firms to sustain the collusive outcome. (iii) What is one factor that will determine the likelihood that the firms are able to sustain the collusive outcome? (4 marks) Suppose there are two sound recording companies, each of which has two possible actions to set either a 'low price' or 'high price'. Where both firms choose 'low price' this can be thought of as the competitive outcome, and where both firms choose 'high price' this can be thought of as the collusive outcome. Payoffs (profits) are as follows: Warner Low price High price Sony Low price 0,0 -10,60 High price 60,-10 50,50 a) Suppose the two sound recording companies interact once in the market and must choose their strategies simultaneously. Identify the Nash equilibrium of the game and explain why this is the Nash equilibrium. (3 marks) b) Suppose the two sound recording companies interact once in the market and choose their strategies sequentially. Warner chooses its strategy first, and Sony chooses its strategies second. (i) Draw the game tree that represents this game. (ii) What is the rollback equilibrium of the game? (4 marks) c) Suppose that the two sound recording companies interact once in the market. Suppose that, in the sequential version of the game, Sony has the opportunity to choose whether to advertise its product prior to both of the sound recording companies making their choices of prices. (That is, Sony chooses whether to advertise, then Warner chooses its price strategy, and then Sony chooses its price strategy.) If Sony does advertise then it incurs a cost of 10. The benefit of advertising is that it raises the payoff to Sony by 20 when both Sony and Warner choose 'High price'. (i) Draw the game tree that represents this game. (ii) What is the rollback equilibrium of the game? (4 marks) d) Suppose that the two sound recording companies interact indefinitely in the market. In each time period in which they interact, they choose their strategies simultaneously. (i) Suggest a strategy that the sound recording firms might adopt to sustain the collusive outcome as a Nash equilibrium. (ii) Give some intuition for why your suggested strategy for each firm will allow the firms to sustain the collusive outcome. (iii) What is one factor that will determine the likelihood that the firms are able to sustain the collusive outcome? (4 marks)

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a To find the Nash equilibrium of the game we need to look for strategies where neither firm has an incentive to unilaterally change its action given ... View the full answer