The mixed strategy Nash equilibrium of the television news scheduling game

We characterize the unique mixed-strategy equilibrium of an extension of the "television news sheduling game" of Cancian, Bergström and Bills (1995) where viewers want to watch the first newscast broacast after they return home. A fraction of the viewers record randomly one of the newscast to watch them in case they are too late. At equilibrium, neither of the two stations broadcasts its evening news in the first part of the evening and the density function is strictly decreasing.