Electoral Competition with abstention. Think about the following version of the Electoral Competition game. The two players have the same strategies as before. The payoffs, again, are the total number of votes. However, the distribution of voters is different: there are 500 voters supporting policies 1 and 9 each, and, as before, 100 for each policy in {2, ..., 8}, for a total of 1700 voters. And so, for example, if D chooses 3 and R chooses 5, then D gets 750 (all votes from 1,2,3 and 50 votes from 4), and R gets 950 votes (all votes from 5,6,7,8 and 50 votes from 4).

(a) Which strategies are strictly dominated for R and D?

(b) Which strategies are in BR and BRR, for all n? Now, suppose that the distribution of voters is as above, with 1700 voters, the voters vote for the closer of the two parties (and split if indifferent) as before, but only if the policies are 0 or 1 spaces away. And so, for example, if D chooses 3 and R chooses 5, then D gets 250 and R gets 250 as well.

(c) Is 5 strictly dominated in this new game? If so, by which other strategy? (Note that the game is symmetric, so the answer is the same for D and R).

(d) (hard!) What are all the strictly dominated strategies in this new game? (Note as above).