PLEASE EXPLAIN THOROUGHLY. Use game theory and Nash Equil concepts. Last tutor did not explain properly, I know the answer but I want to understand the process clearly.

There is an election with three candidates. In this election, there is a single issue that voters care about. Imagine that voters are spread out evenly on a number line on the interval [0,1]. All three candidates simultaneously pick their position on the line and voters vote for the candidate closest to them. If two or more candidates are equally close to a voter, then that voter splits her vote between the candidates. If candidates get the same number of votes, then a winner will be determined randomly with each candidate having an equal likelihood of winning. Assume that the candidates all wish to maximize their share of the votes.

a) (15 points) Does this game have a pure strategy Nash equilibrium? If so, find it. If not, prove it.b) (15 points) Now consider the four candidate case. Will this game have a PSNE? Prove your result.