Reference no: EM131097710

Suppose there are two candidates disputing election in a linear city defined on the interval [0, 1]. There is a continuum of voters uniformly distributed on the interval [0, 1]. Voters closer to the point 0 prefer more conservative candidates, and voters closer to 1 prefer more liberal candidates. Voters closer to the midpoint 1/2 prefer moderate candidates (i.e., not excessively conservative and not excessively liberal candidates). During the election campaign, each candidate must simultaneously decide whether to adopt a more conservative or more liberal posture. More precisely, they must pick a point between [0, 1], where a point closer to 0 means the candidate is more conservative, and a point closer to 1 means the candidate is more liberal. Assuming that candidate 1 picks point x1 and candidate 2 picks point x2, then an elector located at point x will vote for candidate 1 iff |x−x1| < |x−x2| (i.e., iff x is closer to x1 than to x2), and he will vote for candidate 2 iff |x−x1| > |x−x2| (i.e., iff x is closer to x2 than to x1). We assume that a candidate wins the election if he gets more than 1/2 of the votes. If both candidates get 1/2 of the votes, then there is a fair coin toss to decide who wins. Obviously, each candidate strictly prefers winning over loosing. Given the environment described above, find the unique pure strategy NE from this game (show your work).