EXERCISE 75.1 (Electoral competition between candidates who care only about the winning position) Consider the variant of Hotelling's model in which the can- didates (like the citizens) care about the winner's position, and not at all about winning per se. There are two candidates. Each candidate has a favorite posi- tion; her dislike for other positions increases with their distance from her favorite position. Assume that the favorite position of one candidate is less than m and the favorite position of the other candidate is greater than m. Assume also that if the candidates tie when they take the positions x₁ and x2, then the outcome is the compromise policy (x₁+x2). Find the set of Nash equilibria of the strategic

EXERCISE 75.1 (Electoral competition between candidates who care only about the winning position) Consider the variant of Hotelling's model in which the can- didates (like the citizens) care about the winner's position, and not at all about winning per se. There are two candidates. Each candidate has a favorite posi- tion; her dislike for other positions increases with their distance from her favorite position. Assume that the favorite position of one candidate is less than m and the favorite position of the other candidate is greater than m. Assume also that if the candidates tie when they take the positions x₁ and x2, then the outcome is the compromise policy (x₁+x2). Find the set of Nash equilibria of the strategic

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 4CQQ

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3.17. Consider the social choice function that selects as a winner thecandidate (or candidates) with the most second-place votes.(a) Show that this method violates monotonicity.(b) Show that this method violates the Pareto criterion.(c) Show that this method is anonymous and neutral.
The magazine Science 84 planned to announce a contest in which anyonecould submit a request for either $20 or $100. If fewer than 20% of the submissions requested $100, then everybody would receive what they requested. If 20% or more asked for $100, then everybody would get nothing. Although the magazine wound up not running the contest, because Lloyds of London was unwilling to insure against losses, we can still analyze what equilibrium would predict. Suppose 100,000 people might participate in the contest, and assume that payoffs are measured in money.a. Assume that every possible participant submits a request for either $20or $100. Find a Nash equilibrium.b. Now suppose that a request form comes only with the purchase of Science 84 and that the magazine costs $21.95. Then each person’s strategy set has three elements: do not buy the magazine, buy the magazine and submit a request for $20, and buy the magazine andsubmit a request for $100. Suppose zero value is attached to…
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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Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?
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Mr. and Mrs. Smith vote opposite in presidential elections in a swing state. Assign 1 point for voting your preferred candidate and 0 points if you don’t vote. If you don’t want your candidate to lose, what is the Nash equilibrium in this situation?
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