Problem 2 There are three major network affiliate television stations in Hicksville: RBC, CBC and MBC. All three stations have the option of airing the evening network-news program live at 6:00 pm or in a delayed broadcast at 7:00 pm. By regulation, they may not choose other times. Each station’s objective is to maximize its viewing audience, in order to maximize the station’s advertising revenue. The table below gives the percentage of Hicksville’s total population “captured” by each station as a function of the time at which each news program is shown. The numbers do not sum to 100 since not everyone always watches TV.
Times Chosen Audience Capture MBC RBC CBC MBC RBC CBC 6:00 pm 6:00 pm 6:00 pm 32 14 24 6:00 pm 6:00 pm 7:00 pm 27 8 30 6:00 pm 7:00 pm 6:00 pm 24 30 16 6:00 pm 7:00 pm 7:00 pm 50 13 12 7:00 pm 6:00 pm 6:00 pm 30 16 24 7:00 pm 6:00 pm 7:00 pm 24 30 16 7:00 pm 7:00 pm 6:00 pm 14 30 23 7:00 pm 7:00 pm 7:00 pm 32 14 24
1) Suppose that the choices of all three stations are made simultaneously. Find the Nash equilibrium(s). (Hint: Try to set this up so it looks more like a normal form game. To do this for three players, use two 2*2 matrices: let MBC choose the matrix, RBC the row and CBC the column).
2) Suppose now that the game is played sequentially. MBC moves first. RBC moves second and CBC moves third. Each station can observe all previous moves before making her choice. Explain what will happen.
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