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2 candidates compete by selecting a location in the interval [0,1]. Whichever location is closer to...

2 candidates compete by selecting a location in the interval [0,1]. Whichever location is closer to the median voter wins. The median voter is a random variable drawn from the uniform distribution on [0,1]. In class we assume that the utility to candidate 1 from the location of the winning positin, w is –(0-w)^2, and the utility to candidate 2 from the winning location w is –(1-w)^2

2. Reconsider the model of 2 candidate competition (over school locations) with candidates that face uncertainty about the location of the median voter. In particular both candidates believe the median, m is uniformly distributed on the unit interval (a) First assume that the candidates care only about winning (obtain ing a payoff of 1 from a win, from a tie and 0 from losing). Find the Nash equilibria to this game (b) Now assume that the candidates care about policy and winning So candidate l obtains utility of-r+ γ if she wins and a payoff of -a2 if she does not win. Simmilarly, candidate 2 obtains payoff -(1 - r2)2 y if she wins and payoff (1- if she does not win. The parameter y should be taken as positive but small. Say as much as you can about how best responses and the Nash equlibrium depend on the magnitude of γ

answer both a) AND b) please

2. Reconsider the model of 2 candidate competition (over school locations) with candidates that face uncertainty about the location of the median voter. In particular both candidates believe the median, m is uniformly distributed on the unit interval (a) First assume that the candidates care only about winning (obtain ing a payoff of 1 from a win, from a tie and 0 from losing). Find the Nash equilibria to this game (b) Now assume that the candidates care about policy and winning So candidate l obtains utility of-r+ γ if she wins and a payoff of -a2 if she does not win. Simmilarly, candidate 2 obtains payoff -(1 - r2)2 y if she wins and payoff (1- if she does not win. The parameter y should be taken as positive but small. Say as much as you can about how best responses and the Nash equlibrium depend on the magnitude of γ
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Ans :- Reconsider the model of 2 candidate competition with candidates that face uncertainty about the location of the median voter. In particular both candidates believe the median, m is uniformly distributed on the unit interval.

Condidcate-1 Cl winelose NE to this (game is (win e ,tose),C Lose, Lose b) Candidate- 1 2 2. Candidate-2 ÷ Let p be he peobabiliy Jhat playe wine s (I-P) In ne peobabiliHy that playe* 2 wine, xpected Payoht , candidate 4 CE.) Bu esponse ^uncHon d candidate t is 2) ot candidate 2. CE Similcel expeded ραγο# 乂2.hcee ose LLoe, winedependen+ the magnitude aț

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