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Consider an election with three voters labeled 1, 2,3 and three candidates: L from the left wing party, Rfrom the right wing party, and C from the center party. Voters get utility from each candidate winning as follows: |LCR u1(-) | x u2(:)| 2 u3(:) | z where r > y > z. Each voter selects a candidate and the candidate with the most votes wins. In the case of a tie, all candidates with the most votes win with equal probability. (a) List the pure strategies for each player. Which of them are strictly dominated? Which of them are weakly dominated? (b) Is there a pure strategy Nash equilibrium of the game where L wins outright (without a tie)? Explain why or why not.

Consider an election with three voters labeled 1, 2,3 and three candidates: L from the left wing party, Rfrom the right wing party, and C from the center party. Voters get utility from each candidate winning as follows: |LCR u1(-) | x u2(:)| 2 u3(:) | z where r > y > z. Each voter selects a candidate and the candidate with the most votes wins. In the case of a tie, all candidates with the most votes win with equal probability. (a) List the pure strategies for each player. Which of them are strictly dominated? Which of them are weakly dominated? (b) Is there a pure strategy Nash equilibrium of the game where L wins outright (without a tie)? Explain why or why not.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider an election with three voters labeled 1, 2, 3 and three candidates: L from the left wing party, Rfrom the right wing party, and C from the center party. Voters get utility from each candidate winning as follows: LC R U1(:) | x U2(:) | 2 u3(:) | z Y where r > y > z. Each voter selects a candidate and the candidate with the most votes wins. In the case of a tie, all candidates with the most votes win with equal probability. (a) List the pure strategies for each player. Which of them are strictly dominated? Which of them are weakly dominated? (b) Is there a pure strategy Nash equilibrium of the game where L wins outright (without a tie)? Explain why or why not.
Transcribed Image Text:Consider an election with three voters labeled 1, 2, 3 and three candidates: L from the left wing party, Rfrom the right wing party, and C from the center party. Voters get utility from each candidate winning as follows: LC R U1(:) | x U2(:) | 2 u3(:) | z Y where r > y > z. Each voter selects a candidate and the candidate with the most votes wins. In the case of a tie, all candidates with the most votes win with equal probability. (a) List the pure strategies for each player. Which of them are strictly dominated? Which of them are weakly dominated? (b) Is there a pure strategy Nash equilibrium of the game where L wins outright (without a tie)? Explain why or why not.
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