Consider the following game in the build up to an election. The incumbent right-wing politician must first decide whether to occupy a right-wing or a left-wing stance on a particular policy. After the incumbent has made this decision, the left-wing challenger must then make the same choice. If both choose the same policy stance, the incumbent will stay in office. If both choose a different policy, the challenger will win the election and take office. The value of winning the election is 10, while the loser will get a value of 0. However, if a politician chooses a policy that is different from their own view, they get a value of -5. Where would the Subgame Perfect Nash Equilibrium be in this game? (Hint: Draw the game tree, and form the payoffs based on the information about the value of winning an election and choosing E

Consider the following game in the build up to an election. The incumbent right-wing politician must first decide whether to occupy a right-wing or a left-wing stance on a particular policy. After the incumbent has made this decision, the left-wing challenger must then make the same choice. If both choose the same policy stance, the incumbent will stay in office. If both choose a different policy, the challenger will win the election and take office. The value of winning the election is 10, while the loser will get a value of 0. However, if a politician chooses a policy that is different from their own view, they get a value of -5. Where would the Subgame Perfect Nash Equilibrium be in this game? (Hint: Draw the game tree, and form the payoffs based on the information about the value of winning an election and choosing E

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter31: Public Choice And Special Interet Group Politics

Section: Chapter Questions

Problem 6QP

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Mr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 30 units of utility from a vote for their positions (and lose 30 units of utility from a vote against their positions). However, the bother of actually voting costs each 15 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mr. Ward Vote Don't Vote Mrs. Ward Vote Mr. Ward-15, Mrs. Ward: -15 Mr. Ward: 30, Mrs. Ward: 15 The Nash equilibrium for this game is for Mr. Ward to payoff of False Don't Vote Mr. Ward: 15, Mrs. Ward: -30 Mr. Ward: 0, Mrs. Ward: 0 units of utility and Mrs. Ward receives a payoff of This agreement not to vote. Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would decrease utility for each spouse, compared to the Nash equilibrium from the previous part of the question. O True and for Mrs. Ward to units of utility a Nash equilibrium, Under this outcome, Mr.…
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Exercise 1.12. Consider the following game. There is a club with three members: Ann, Bob and Carla. They have to choose which of the three is going to be president next year. Currently Ann is the president. Each member is both a candidate and a voter. Voting is as follows: each member votes for one candidate (voting for oneself is allowed); if two or more people vote for the same candidate then that person is chosen as the next president; if there is complete disagreement, in the sense that there is exactly one vote for each candidate, then the person from whom Ann voted is selected as the next president. (a) Represent this voting procedure as a game frame, indicating inside each cell of each table which candidate is elected. (b) Assume that the players' preferences are as follows: Ann > Carla Ann Carla Bob Bob>Bob Ann, Bob Carla Ann Carla Carla. Using utility values 0, 1 and 2, convert the game frame into a game. Ann Bob. (c) Apply the IDWDS to the game of part (b). Is there a weak…
Exercise 1.12. Consider the following game. There is a club with three members: Ann, Bob and Carla. They have to choose which of the three is going to be president next year. Currently Ann is the president. Each member is both a candidate and a voter. Voting is as follows: each member votes for one candidate (voting for oneself is allowed); if two or more people vote for the same candidate then that person is chosen as the next president; if there is complete disagreement, in the sense that there is exactly one vote for each candidate, then the person from whom Ann voted is selected as the next president. (a) Represent this voting procedure as a game frame, indicating inside each cell of each table which candidate is elected. (b) Assume that the players' preferences are as follows: AnnAm Carla Ann Bob, Carla Bob Ann, Bob Carla Ann Caria Carla. Using utility values 0, 1 and 2, convert the game frame into a game. (c) Apply the IDWDS to the game of part (b). Is there a weak iterated…
Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 6 units of utility from a vote for their positions (and lose 6 units of utility from a vote against their positions). However, the bother of actually voting costs each 3 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mrs. Ward Vote Don't Vote Mr. Ward Vote Mr. Ward: -3, Mrs. Ward: -3 Mr. Ward: 3, Mrs. Ward: -6 Don't Vote Mr. Ward: -6, Mrs. Ward: 3 Mr. Ward: 0, Mrs. Ward: 0 The Nash equilibrium for this game is for Mr. Ward to and for Mrs. Ward to . Under this outcome, Mr. Ward receives a payoff of units of utility and Mrs. Ward receives a payoff of units of utility. Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would decrease utility for each spouse, compared to the Nash equilibrium from the previous part of the question. True…
Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 4 units of utility from a vote for their positions (and lose 4 units of utility from a vote against their positions). However, the bother of actually voting costs each 2 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mrs. Ward Vote Don't Vote Mr. Ward Vote Mr. Ward: -2, Mrs. Ward: -2 Mr. Ward: 2, Mrs. Ward: -4 Don't Vote Mr. Ward: -4, Mrs. Ward: 2 Mr. Ward: 0, Mrs. Ward: 0 The Nash equilibrium for this game is for Mr. Ward to (vote/not vote) and for Mrs. Ward to (vote/not vote) . Under this outcome, Mr. Ward receives a payoff of ____ units of utility and Mrs. Ward receives a payoff of ____ units of utility. Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would increase utility for each spouse, compared to the Nash…
Match the following according to the criterion. If a candidate receives [ Choose ] more than half the first- place votes in an election, then that candidate should be declared the winner. If a candidate is favored [ Choose ] when compared separately with every other candidate in an election, then that candidate should be declared the winner. If a candidate wins an [ Choose] election and, in a reelection, the only changes are changes that favor the candidate, then that candidate should win the reelection. If a candidate wins an [ Choose ] election and, in a recount, the only changes are that one or more of the other candidates are removed from the ballot, then that candidate should still win the election.
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