1.8. 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 cam- paign platform (i.e., a point on the line between x = 0 and x = 1). The voters observe the candidates' choices, and then each voter votes for the candidate whose platform is closest to the voter's position on the spectrum. If there are two candidates and they choose platforms x1 .3 and x2 .6, for example, then all voters to the left of x = .45 vote for candidate 1, all those to the right vote for candidate 2, and candidate 2 wins the elec- tion with 55 percent of the vote. Suppose that the candidates = 11 =

1.8. 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 cam- paign platform (i.e., a point on the line between x = 0 and x = 1). The voters observe the candidates' choices, and then each voter votes for the candidate whose platform is closest to the voter's position on the spectrum. If there are two candidates and they choose platforms x1 .3 and x2 .6, for example, then all voters to the left of x = .45 vote for candidate 1, all those to the right vote for candidate 2, and candidate 2 wins the elec- tion with 55 percent of the vote. Suppose that the candidates = 11 =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 80% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 75% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 30% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 65% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson City Rural Robinson CityRural Is the game strictly determined? YesNo (b) Find the optimal strategy for both Robinson (row) and Carson (column). P = Q =