Ex. 4 Strength Can Be WeaknessA three-person committee has to choose a winner for a prize. After some debate, thereare three candidates still under consideration. Let's call these candidates a, b and c, andcall those committee members 1, 2 and 3. The committee members only care about whichcandidate wins the prize, and their preferences as follows: member 1 prefers a to b andb to c; member 2 prefers c to a and a to b; and member 3 prefers b to c and c to a. Therules of the competition say that the committee should first apply majority vote (secretballot, one member one vote) and the candidate with the most votes wins. If the vote istied, that is, the majority rule select a unique winning candidate, then the winner willbe the candidate for whom member 1 voted. Thus, it might seem that member 1 has anadvantage.(1) Write down the strategic form of this voting game. [You may assign any numberto the payoff of each voter, as long as it is consistent with her preference order.](2) For each voter, which strategies are weakly or strictly dominated? [You may wantto pay extra attention to voter 1.](3) Now consider the reduced game in which all weakly and strictly dominated strate-gies have been removed from the original game. For each voter, which strategies arenow weakly or strictly dominated? What is the outcome predicted by the processof iterated elimination of dominated strategies? Compare this outcome to voter l'spreferences and comment.

Dominated Strategy: In game theory, a strategy is said to be dominated if there exists another…

Ex. 4 Strength Can Be Weakness A three-person committee has to choose a winner for a prize. After some debate, there are three candidates still under consideration. Let's call these candidates a, b and c, and call those committee members 1, 2 and 3. The committee members only care about which candidate wins the prize, and their preferences as follows: member 1 prefers a to b and b to c; member 2 prefers c to a and a to b; and member 3 prefers b to c and c to a. The rules of the competition say that the committee should first apply majority vote (secret ballot, one member one vote) and the candidate with the most votes wins. If the vote is

Ex. 4 Strength Can Be Weakness A three-person committee has to choose a winner for a prize. After some debate, there are three candidates still under consideration. Let's call these candidates a, b and c, and call those committee members 1, 2 and 3. The committee members only care about which candidate wins the prize, and their preferences as follows: member 1 prefers a to b and b to c; member 2 prefers c to a and a to b; and member 3 prefers b to c and c to a. The rules of the competition say that the committee should first apply majority vote (secret ballot, one member one vote) and the candidate with the most votes wins. If the vote is

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C. Max prefers A to B to C. Sally prefers B to A to C. To decide which restaurant to go to, the friends adopt the following procedure: First, Max eliminates one of three choices. Then, Sally decides among the two remaining choices. Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining). a.Write down the extensive form (game tree) to represent this game. b.If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be? c.What is the subgame-perfect equilibrium of the above game? d. Does your answer in b. differ from your answer in c.? Explain why or why not. Only typed Answer
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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.
Mr. and Mrs. Ward typically vote oppositely in elections and so their votes "cancel each other out." They each gain 24 units of utility from a vote for their positions (and lose 24 units of utility from a vote against their positions). However, the bother of actually voting costs each 12 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward. Mr. Ward Vote Vote Mrs. Ward Mr. Ward: -12, Mrs. Ward: -12 Don't Vote Mr. Ward: -24, Mrs. Ward: 12 The Nash equilibrium for this game is for Mr. Ward to payoff of Don't Vote Mr. Ward: 12, Mrs. Ward: -24 Mr. Ward: 0, Mrs. Ward: 0 units of utility and Mrs. Ward receives a payoff of and for Mrs. Ward to units of utility. Under this outcome, Mr. Ward receives a
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8) Consider the following game: There are 10 players. Each player is asked to write a number between 0 and 100. The player whose choice is closest to half of the average is the winner. Describe the game and discuss what would you expect to be the average number if the game were played in class with your colleagues. Do you expect them to play the Nash equilibrium strategy? Explain.
26. Consider the following game. There are ten churches in town: nine are Catholic and one is Eastern Orthodox. All churches conduct their services at 10am on Sunday morning. You and your friend, without communication, agree to meet at a church service. If you fail to meet at the same church, then you are sad. What is this game's focal point? Remember that you cannot communicate about this. (A) You meet at any of the Catholic churches. (B) You meet at any of the churches – denomination does not matter. (C) You meet at the Orthodox church. (D) There is no focal point. 27. Which of the following is the best example of Skin in the Game? (A) A politician retires to serve on the board of governors of a prestigious think tank. (B) A wealthy man donates his savings to charity. (C) A general leads his troops into battle. (D) Billie Eilish creates another cringe music video. 28. Public choice theory makes assumptions about the motives of politicians, firms, voters, and bureaucrats. Which of…
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