09 Jul Disney and Nickelodeon
There are two cartoon channels, Disney and Nickelodeon , providing content to two audience members, Jimmy and Karen. The kids have limited time because of HW and can only watch one channel. Jimmy and Karen care about the channel’s quality, but also about whether their friends watch it: they like to talk among themselves about the channel’s content. Let Qj denote the quality of channel j and Wj indicate whether the other audience member watches channel j. Then an audience member’s payoff from watching channel j is the sum: Qj +Wj . The audience members decide independently which channel to watch; they must each choose exactly one. (1) If QX = 0.5, what is member Jimmy’s payoff from watching Disney channel if Karen also watches it? What is Jimmy’s payoff from Disney if Karen does not watch it? (2) Think of the audience members’ choice of channels as a strategic form game. For QX = 1 and QY = 0.5, what are the pure strategy equilibria? Is there a mixed Nash equilibrium? (You do not have to find it.) (3) For QX = 1 and QY = 0.5, explain why it is possible that both players watch the lower quality channel in equilibrium. (4) For any values of QX > 0 and QY > 0, is there any pure strategy equilibrium in which players watch different channels? (5) Suppose viewers no longer care about what channel the other watches. That is, a viewer’s utility from watching channel j is simply Qj . Now is there a Nash equilibrium where both players watch the lower quality channel? (mixed and pure equilibrium)
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