Consider a Downsian electoral competition over the line [-1,1)] where there are 11 voters.Each voter has a single-peaked preferences over the policies. Voter l's peak is at -1, voter 2's at-0.8, .., voter 6's at 0, voter 7's at 0.2, ..., and voter 11's at 1. Suppose there are two candidates,{D,R} and if they get equal votes the tie is broken by a coin toss that is, both wins the electionwith probability 1/2.(a) What is the Nash Equilibrium of this game?(b) Now suppose that there is an ideological candidate C that positions himself at -1 whateverthe other candidates do. Is there a Nash Equilibrium of the game? If so, what is it?

Game theory is a subfield in economics where rational decision-makers' strategic interactions are…

(a) What is the Nash Equilibrium of this game? (b) Now suppose that there is an ideological candidate C that positions himself at -1 whatever the other candidates do. Is there a Nash Equilibrium of the game? If so, what is it?

(a) What is the Nash Equilibrium of this game? (b) Now suppose that there is an ideological candidate C that positions himself at -1 whatever the other candidates do. Is there a Nash Equilibrium of the game? If so, what is it?

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

Consider a Downsian electoral competition over the line [-1,1)] where there are 11 voters.
Each voter has a single-peaked preferences over the policies. Voter l's peak is at -1, voter 2's at
-0.8, .., voter 6's at 0, voter 7's at 0.2, ..., and voter 11's at 1. Suppose there are two candidates,
{D,R} and if they get equal votes the tie is broken by a coin toss that is, both wins the election
with probability 1/2.
(a) What is the Nash Equilibrium of this game?
(b) Now suppose that there is an ideological candidate C that positions himself at -1 whatever
the other candidates do. Is there a Nash Equilibrium of the game? If so, what is it?

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