Election is taking place in a city. There are two candidates, Land R. There are 100 voters numbered 1 to 100. Of them, 1 to 60 prefer candidate R, while 61 to 100 prefer candidate L. Voters know all of these things-the number of voters preferring L and R, and their own preference. Every voter receives a payoff of 1 if their preferred candidate wins and 0 otherwise. Winner is the candidate who wins the highest number votes. Voting is costly, and a voter incurs a cost of 18 to go to the booth and wait. In case of a tie, each candidate is chosen with a probability 12. Which of the following is/are true? (a) In every pure strategy Nash equilibrium, R wins with a positive probability. (b) There is a pure strategy Nash equilibrium in which L wins with a positive probability. (c) There is a pure strategy Nash Equilibrium in which every R - preferring voter goes to vote. (d) There is a pure strategy Nash Equilibrium in which exactly 2 voters go to vote and the winner is L. (e) There is no pure strategy equilibrium in this game.
Election is taking place in a city. There are two candidates, Land R. There are 100 voters numbered 1 to 100. Of them, 1 to 60 prefer candidate R, while 61 to 100 prefer candidate L. Voters know all of these things-the number of voters preferring L and R, and their own preference. Every voter receives a payoff of 1 if their preferred candidate wins and 0 otherwise. Winner is the candidate who wins the highest number votes. Voting is costly, and a voter incurs a cost of 18 to go to the booth and wait. In case of a tie, each candidate is chosen with a probability 12. Which of the following is/are true? (a) In every pure strategy Nash equilibrium, R wins with a positive probability. (b) There is a pure strategy Nash equilibrium in which L wins with a positive probability. (c) There is a pure strategy Nash Equilibrium in which every R - preferring voter goes to vote. (d) There is a pure strategy Nash Equilibrium in which exactly 2 voters go to vote and the winner is L. (e) There is no pure strategy equilibrium in this game.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Election is taking place in a city. There are two
candidates, Land R. There are 100 voters numbered 1
to 100. Of them, 1 to 60 prefer candidate R, while 61
to 100 prefer candidate L. Voters know all of these
things-the number of voters preferring L and R, and
their own preference. Every voter receives a payoff of 1
if their preferred candidate wins and 0 otherwise.
Winner is the candidate who wins the highest number
votes. Voting is costly, and a voter incurs a cost of 18 to
go to the booth and wait. In case of a tie, each
candidate is chosen with a probability 12. Which of the
following is/are true?
(a) In every pure strategy Nash equilibrium, R wins with
a positive probability.
(b) There is a pure strategy Nash equilibrium in which L
wins with a positive probability.
(c) There is a pure strategy Nash Equilibrium in which
every R - preferring voter goes to vote.
(d) There is a pure strategy Nash Equilibrium in which
exactly 2 voters go to vote and the winner is L.
(e) There is no pure strategy equilibrium in this game.
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