$6.$ HOTELLING'S MODEL $(20$PTS$)$ Consider the Hotelling$-$Downs electoral competition model with four players, each chooses a policy position in the interval $(0\mathrm{.}1]$ to maximize their probability of winning the election. Now assume that the voters' ideal policies are distributed uniformly over $[0,1].($This means that, for all $0<$ a $<$ b $<1,$ the proportion of the voters with ideal policies between a and b is equal to b $-$ a$.$ Thus, the median voter now has ideal policy $1.)$ n n n V O $=$v $$ Done M $(4)$ Is $(1,1,1,1)$ a Nash equilibrium when there are four players seeking to maximize their vote share? Explain. $(5$pts