Consider the following game. There are ten political positions, 1, ,10, from the most liberal to the most conservative. Two politicians simultaneously choose what position they pick in order to maximize the percentage of votes they can get. 10% of voters are at each position. Voters will vote for the politician they are closer to. If voters at a position are equally distanced from the two politicians, then 5% vote for one and 5% vote for the other. If two politicians choose the same position then they each get 50% of the votes.

(a) List dominated strategies. If there is none, write "none."

(b) List dominant strategies. If there is none, write "none."

(c) Find all (pure-strategy) Nash equilibria of this game.