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elvia261
elvia261
01.10.2019 • 
Mathematics

Consider a population of voters uniformly distributed along the ideological spectrum from left (x = 0) to right (x = 1). each of the candidates for a single office simultaneously chooses a campaign platform (i.e., a point on the line between x = 0 and x = 1). the voters observe the candidates choices, and each voter votes for the candidate whose platform is closest to the voters position on the spectrum. if there are two candidates and they choose platforms x1 = 0.3 and x2 = 0.6, for example, then all voters to the left of x = 0.45 vote for candidate 1, all those to the right vote for candidate 2, and candidate 2 wins the election with 55% of vote. suppose that the candidates care only about being elected. if there are two candidates, what is the pure strategy nash equilibrium?

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