2. (9 %)

Consider two players in a game: Legislator (L) and the Judiciary (J). The Legislator and the Judiciary negotiate a bill $B$ to be executed from a policy space $\mathcal{B} = [0,10]$, where $B0 = 0$ is the status quo. Legislator's favorite policy is $BL^* = 9$, and Judiciary's favorite policy is $B_J^* = 3$.

The game has 2 stages and proceeds as follows:







Define player \( i \)'s payoff as \( \pi_i = |B_i^* - B| \). Assume that the Judiciary will not reject the bill if rejecting the bill is indifferent to her.