Median Voter

Consider a school-board election in which each citizen votes for the candidate whose expressed budget position is closest to the citizen's preferred budget. The distribution of voter preferences is uniform, with 10 voters in each $1 interval from $1 to $11. True to their names, Penny initially proposes a small budget ($3) and Buck proposes a large budget ($9).

1. Is the initial set of proposals ($3 and $9) a Nash equilibrium? Illustrate with a unilateral deviation by Penny of +$3.
2. Describe the Nash equilibrium in terms of proposed budgets by Penny and Buck.