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EXERCISE 73.1 (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 position; her dislike for other positions increases with their distance from her favorite po- sition. 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 com- promise 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 ei- ther 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).)

EXERCISE 73.1 (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 position; her dislike for other positions increases with their distance from her favorite po- sition. 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 com- promise 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 ei- ther 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).)

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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EXERCISE 73.1 (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 position; her dislike for other positions increases with their distance from her favorite po- sition. 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 com- promise 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 ei- ther 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).)
Transcribed Image Text:EXERCISE 73.1 (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 position; her dislike for other positions increases with their distance from her favorite po- sition. 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 com- promise 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 ei- ther 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).)
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