In some presidential elections, there is a serious third-party candidate.
In some presidential elections, there is a serious third-party candidate. In 1992, Ross Perot, running as an independent against Democratic nominee Bill Clinton and Republican nominee George Bush, garnered a respectable 19% of the vote. More recent third-party presidential at- tempts were made by Ralph Nader as the Green Party nominee in 2000 and 2004. In light of such instances, consider a model of electoral com- petition with three candidates, denoted D, R, and I(ndependent). As in Section 6.2, each candidate chooses a position from the interval [0,1]. A candidate receives a payoff of 1 if he receives more votes than the other two candidates (so that he wins for sure), a payoff of if he is tied with one other candidate for the most votes, a payoff of if all three candi- dates share the vote equally, and a payoff of zero if his share of the vote is less than another candidate’s (so that he loses for sure). Assume that voters vote for the candidate whose position is nearest their own. Is it a Nash equilibrium for all three candidates to locate at