(28 pts) Sequential winner takes all advertising: Exactly two rms are competing by sequentially choosing the amount of money to spend on advertising in a market. First from one chooses an amount of advertising, at, from the set of whole numbers (nonnegative integers) horn '0 to 100. That is a: can be any element from {0, 1, 2, . . ., 100}. Firm two observes this choice and then chooses an amount of advertising, 02, from the set of whole numbers (nonnegative integers) from 0 to 100. Each rm produces at '0 cost; each rm's only cost is the amount of money it spends on advertising. The value of the market is $80. If the amounts of , i ' advertising are different, the entire value of the market will go to the: rm with the highest level of advertising. If the amounts of advertising are the same, half the value of the market will go to each firm. For instance, if rm one chooses an = 20 and rm two chooses a2 =~ 30, the entire market will go to rm two. Firm one's prot will by 20 and rm two's prot will be 80 30 = 50. Sequential winner takes all advertising: Exactly two rms are competing by sequentially choosing the amount of money to spend on advertising in a market. First rm one chooses an amount of advertising, a1, from the set of whole numbers (nonnegative integers) from 0 to 100. That is on can be any element from {0, 1, 2, . . ., 100}. Finn two observes this choice and then chooses an amount of advertising, a2, om the set of whole numbers (nonnegative integers) from O to 100. Each firm produces at 0 cost; each rm's only cost is the amount of money it spends on advertisingf'l'he value of the market is $80. If the amounts of advertising are different, the entire value of the market will go to the rm with the highest level of advertising. If the amounts of advertising are the same, half the value of the market will go to each rm. 4 'f S 40 . . . . . c. 15 a = 40412 = 0 l a, a Nash equilibrium? If so, is it 3 11 if a, > 40 ' subgame perfect? Clearly demonstrate your logic. - ~ 7 (1. Clearly describe all subgame perfect Nash equilibria. You do not need to explicitly list firm two's action contingent on each of rm one's possible actions, but you do need to describe them verbally or mathematically. Clearly demonstrate your logic