3. 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 S- 2: {1,2, .. . , 10}. 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