Question

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 1 obtains utility of -y if she wins and a payoff of -r if she does not win. Simmilarly, candidate 2 obtains payoff -(1-2 + if she wins and payoff-(1-) if she does not win. The parameter γ 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 y MODEL: 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

Answer 1