Hotelling’s Continuous Model: Consider Hotelling’s model, in which citizens are a continuum of…

Hotelling’s Continuous Model: Consider Hotelling’s model, in which citizens are a continuum of voters on the interval A = [−a, a], with uniform distribution U(a).

a. What is the best response of candidate i if candidate j is choosing aj > 0?

b. Show that the unique Nash equilibrium is a1 = a2 = 0.

c. Show that for a general distribution F(.) over [−a,a] the unique Nash equilibrium is where each candidate chooses the policy associated with the median voter.