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# There are three major network affiliate television stations in

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.