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:

Stage 1: The Legislator chooses a bill $B_L \in [0,10]$.

Stage 2: After seeing $BL$, the Judiciary can choose to pass or reject the bill. If the bill is passed, the executed bill will be $B = BL$. If the bill is rejected, the society goes back to the status quo, $B = B_0 = 0$.





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

(a) Under the Subgame Perfect Nash Equilibrium, what is the equilibrium bill passed, \( B_{SPNE} \)?