Each ofnpeople chooses whether or not to become a political candidate, and if so whichposition to take on a 0-1 spectrum.(Assume the positions are perfectly divisible along the spectrum and that they can pick any point in this range, and including the extremes).

There is a continuum of citizens, each of whom has a favourite position; Assume that the citizens are uniformly distributed over the 0-1 spectrum. A candidate attracts the votes of those citizenswhose favourite positions are closer to his position than to the position of any other candidate; ifkcandidates choosethe same position then each receives the fraction 1/kof the votes that the position attracts. The winner of thecompetition is the candidate who receives the most votes. Each person prefers to be the unique winning candidatethan to tie for first place, prefers to tie for first place than to stay out of the competition, and prefers to stay out ofthe competition than to enter and lose.

1. Model as a strategic game and solve for the pure strategy Nash if n=2.
2. Is there a pure strategy Nash if n=4?