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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 Economics, 7th Edition (MindTap Course List)
Principles of Economics, 7th Edition (MindTap Course List)
7th Edition
ISBN:9781285165875
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
Problem 7PA
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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 game that models this situation. (First consider pairs (x₁, x2) of positions for which either x₁ < m and x₂ < m, or x₁ > m and x2 > m. Next consider pairs (x1, x2) for which either x₁ <m < x2, or x2 < m < x₁, then those for which x₁ = m and x2 m, or x₁ m and x2: = m. Finally consider the pair (m, m).) The set of candidates in Hotelling's model is given. The next exercise asks you to analyze a model in which the set of candidates is generated as part of an equilibrium.
Transcribed Image Text: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 game that models this situation. (First consider pairs (x₁, x2) of positions for which either x₁ < m and x₂ < m, or x₁ > m and x2 > m. Next consider pairs (x1, x2) for which either x₁ <m < x2, or x2 < m < x₁, then those for which x₁ = m and x2 m, or x₁ m and x2: = m. Finally consider the pair (m, m).) The set of candidates in Hotelling's model is given. The next exercise asks you to analyze a model in which the set of candidates is generated as part of an equilibrium.
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