Question

Candidates L and R are running for office and only care about winning, not actual policy. The tax rate can take on any value over the interval [0, 1]. Each candidate simultaneously announces their proposed tax rate, Xi. Voters have strong opinions about their preferred tax rate. More specifically, each voter has an ideal tax rate they would like to see implemented, Vj. Voter j will back candidate i if and only if [xi–vj] < [x-i–vj]. Tied elections are determined by a coin flip. Characterize the Nash Equilibrium to this voting game and show that it is unique.

Answer 1