Question

A risk-neutral state representative is choosing whether to run for a seat in Congress. He estimates he has a 1/8 chance of winning if the incumbent chooses to run again, and a 4/7 chance of winning if she does not. If he decides not to run for Congress but instead remain in the state legislature, he estimates he has a 6/7 chance of reelection. (Assume that state law prohibits running for both offices at the same time.) If he values being in Congress twice as much as being in the state legislature, what probability of the incumbent's seeking reelection will make him indifferent between running for the state legislature and running for Congress?

Answer 1