(1) Voters have single-peaked preferences, so we can apply the median voter theorem. Given the distribution of voters' preferences, the median voter's ideal point is 8. Therefore, both candidates will choose position at 8. (2) Yes, both choosing 8 is still a Nash equilibrium. To see this, we show that given the other candidate chooses 8, choosing 8 gives a candidate the highest votes. The vote share when choosing 8 is 1 2 (1 10%) = 45%. (Only the 10% voters with ideal point of 40 will vote for the non-strategic candidate, and the rest voters split their votes equally among the two strategic candidates when they both choose 8.) If a candidate chooses a position other than 8 while the rival's position is 8, the rival will get all the votes from the 60% of the voters with ideal point 8. Therefore the candidate's vote share cannot exceed 45%, therefore, 8 is the best choice