Two candidates, A and B, compete in an election. Of the n citizens, k support candidate A and m = n-k support candidate B. Each citizen decides whether to vote, at a cost, for the candidate she supports, or to abstain. A citizen who abstains receives a payoff of 2 if the candidate she supports win, 1 if this candidate ties for first place, and 0 if this candidate loses. A citizen who votes receives the payoffs 2 C, 1- - c, and -c in these three cases, where 0
Two candidates, A and B, compete in an election. Of the n citizens, k support candidate A and m = n-k support candidate B. Each citizen decides whether to vote, at a cost, for the candidate she supports, or to abstain. A citizen who abstains receives a payoff of 2 if the candidate she supports win, 1 if this candidate ties for first place, and 0 if this candidate loses. A citizen who votes receives the payoffs 2 C, 1- - c, and -c in these three cases, where 0
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Two candidates, A and B, compete in an election. Of the n citizens, k support
candidate A and m = n − k support candidate B. Each citizen decides whether
to vote, at a cost, for the candidate she supports, or to abstain. A citizen
who abstains receives a payoff of 2 if the candidate she supports win, 1 if this
candidate ties for first place, and 0 if this candidate loses. A citizen who votes
receives the payoffs 2 - c, 1 c, and -c in these three cases, where 0 < c < 1.
(a) For k
= m find the set of pure Nash equilibria. (Is the action profile in
which everyone votes a Nash equilibrium?)
(b) What is the set of pure Nash equilibria for k < m?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafade1a9-1f29-4d84-b55a-a57e5a303c8b%2Fe2128965-e698-43c7-a980-a670cb1acdcf%2Fgkd7ma_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Two candidates, A and B, compete in an election. Of the n citizens, k support
candidate A and m = n − k support candidate B. Each citizen decides whether
to vote, at a cost, for the candidate she supports, or to abstain. A citizen
who abstains receives a payoff of 2 if the candidate she supports win, 1 if this
candidate ties for first place, and 0 if this candidate loses. A citizen who votes
receives the payoffs 2 - c, 1 c, and -c in these three cases, where 0 < c < 1.
(a) For k
= m find the set of pure Nash equilibria. (Is the action profile in
which everyone votes a Nash equilibrium?)
(b) What is the set of pure Nash equilibria for k < m?
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