Consider a continuum of voters, each of whom has a bliss point; the distribution of bliss points is described by a c.d.f F(x) on [0, 1]. Each of n people chooses whether or not to become a candidate, and if so which position to take on [0, 1]. Voters vote for the candidate whose position is closer to his bliss point. If k candidates choose the same position or get the most votes, each of them wins with probability 1/k. Otherwise, the candidate receiving the most votes is the winner. Each person prefers to be the unique winning candidate than to tie for the rst place, prefers to tie for the first place than to stay out of the competition, and prefers to stay out of the competition than to enter and lose.

a)Formulate this game as a normal form game.

(b) Find the set of Nash equilibria for n = 2.

(c) Show that there is no pure strategy NE when n = 3