Hotelling's Location Game. Recall the voting game we discussed in class. There are two

candidates, each of whom chooses a position from the set Si := f1; 2; : : : ; 10g. The voters are equally

distributed across these ten positions. Voters vote for the candidate whose position is closest to

theirs. If the two candidates are equidistant from a given position, the voters at that position split

their votes equally. The aim of the candidates is to maximize their percentage of the total vote.

Thus, for example, u1(8; 8) = 50 and u1(7; 8) = 70. [Hint: in answering this question, you do not

need to write out the full payo matrices!]

(a) In class, we showed that strategy 2 strictly dominates strategy 1. In fact, other strategies

strictly dominate strategy 1. Find all the strategies that strictly dominate strategy 1. Explain your

answer. [Hint: try some guesses and see if they work.]

(b) Suppose now that there are three candidates. Thus, for example, u1(8; 8; 8) = 33:_3

and

u1(7; 9; 9) = 73: _ 3. Is strategy 1 dominated, strictly or weakly, by strategy 2. How about by strategy

1

3? Explain. Suppose we delete strategies 1 and 10. That is, we rule out the possibility of any

candidate choosing either 1 or 10, although there are still voters at those positions. Is strategy 2

dominated, strictly or weakly, by any other (pure) strategy si in the reduced game? Explain.