2. Consider the following variation of the Hotelling model. Instead of firms, the pla are candidates seeking election. Voters have preferences indexed by the numbers betw 0 and 1. A candidate chooses a policy between 0 and 1. Given a set of candidates and a of chosen policies, a given voter will vote for the candidate whose policy is closest to t voter's favorite. Voters' favorite policies are uniformly distributed between 0 and 1. for instance, if there are two candidates, candidate one chooses policy 1/4, and candid two chooses policy 5/8, then 7/16 of voters will vote for candidate 1 (those with favo policies between 0 and 7/16), and 9/16 of voters will vote for candidate two (those v favorite policies between 7/16 and 1). If two candidates choose the same policy, they s their votes equally. A candidate wins if she gets a strictly greater share of votes thane of the other candidates. A candidate loses if some other voter gets a strictly greater sh of the votes than she does. In this problem, assume that there are three candidates, 1, 2 and 3, and that they move sequentially: 1 first, then 2, then 3. At a given candidate's turn, she can either choose a policy (a number between 0 and 1, but not equal to 0 or 1), or choose not to run. Candidates prefer winning to being part of a two-way tie, prefer being part of a two-way tie to being part of a three-way tie, prefer being part of a three-way tie to not running, and prefer not running to running and losing. (a) Because of the symmetry of the game, it can be assumed without loss of generality that if candidate 1 enters the race, she chooses a policy xi