three candidates nash equilibrium

Question

Three candidates, Hillary, Ted, and Jeb decide whether to run for president of 2016. Becoming a president has value 10 to each of the candidates. Running a campaign has cost 4 to candidate. If more than one candidate declares her campaign, each of the candidates is equally likely to win the election. (a) Write down the game in matrix form (b) Find all pure-strategy Nash equilibria of the game There are an infinite number of mixed-strategy Nash equilibria in this game. (c) Find one symmetric mixed-strategy Nash equilibrium in which each candidate runs with the same probability. (d) Find one mixed-strategy Nash equilibrium in which one candidate runs with certainty and the other two randomize