We now revisit the electoral competition game. Assume there are now 3 candidates, and that if a group of two or three of the candidates choose the same position, they will split the voters closest to them equally between them. We also change the payoff functions: instead of awarding 1 to the winner and 0 to the losers, assume that each candidate's payoff is equal to the fraction of voters voting for them. Does this game have Nash equilibria (in pure strategies)?

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
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Chapter1: Making Economics Decisions
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you need to show the profitable deviations in each case for some player

the answer should be no nash equilibrium ; but please explain to me in detail

 

NOTE: please DON'T use chatgpt or other AI tools to answer; there's a person who answer my quesitn and his answer is exactly the same as chatgpt; if it's answer from chatgpt I'll downvote; But I'll definitely upvote as long as your explaniton is detailed and you show the profitable deviations in each case for some player. thank you

We now revisit the electoral competition game. Assume there are now 3
candidates, and that if a group of two or three of the candidates choose the
same position, they will split the voters closest to them equally between them.
We also change the payoff functions: instead of awarding 1 to the winner and
0 to the losers, assume that each candidate's payoff is equal to the fraction of
voters voting for them.
Does this game have Nash equilibria (in pure strategies)?
Transcribed Image Text:We now revisit the electoral competition game. Assume there are now 3 candidates, and that if a group of two or three of the candidates choose the same position, they will split the voters closest to them equally between them. We also change the payoff functions: instead of awarding 1 to the winner and 0 to the losers, assume that each candidate's payoff is equal to the fraction of voters voting for them. Does this game have Nash equilibria (in pure strategies)?
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