Question

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

Answer 1

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.