(Voter participation) Consider the game of voter participation. Assume that k ≤ m and that…

(Voter participation) Consider the game of voter participation. Assume that k ≤ m and that each player’s preferences are represented by the expectation of her payoffs given. Show that there is a value of p between 0 and 1 such that the game has a mixed strategy Nash equilibrium in which every supporter of candidate A votes with probability p, k supporters of candidate B vote with certainty, and the remaining m − k supporters of candidate B abstain. How do the probability p that a supporter of candidate A votes and the expected number of voters (“turnout”) depend upon c? (Note that if every supporter of candidate A votes with probability p then the probability that exactly k − 1 of them vote is kpk−1(1 − p).)