2. (This one is for the next problem set - but I'll give it to you ...

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2. (This one is for the next problem set - but I'll give it to you now as you may be paying attention to the primaries) Suppose three candidates, (S)haun, (K)evin, and (B)en, are competing in a primary election. Each of them has enough money to produce one negative ad (targeting one of the other candidates) - assume that there is some probability that a negative ad is effective enough to do away with the candidate. Once a candidate produces an ad, it airs and, if successful, the target candidate is out of the race before he gets a chance to produce his own ad. The candidates that survive have an equal probability of winning the election. Assume the candidates decide sequential and in the order they are listed above.

(a) Assume that the candidates differ in the amount of "dirt' they have on the other candidates (but that the candidate has the same amount of dirt on each of the other candidates). Suppose ps < pK < pb, where Pi is the probability that i's ad is successful, i.e., leads to the targeted candidate to drop out of the race. Find the subgame perfect equilibria of the game.

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