Question $3[15$ points$]$

There are two distinct proposals, A and B $,$ being debated in Washington. The Congress likes proposal A$,$ and the president likes proposal B$.$ The proposals are not mutually exclusive; either or both or neither may become law. Thus, there are four possible outcomes, and the rankings of the two sides are as follows, where a larger number represents a more favored outcome.

a$)(5$ points$)$ The moves in the game are as follows. First, the Congress constructs a bill and decides whether to include A$,$ B$,$ both, or neither policies. Then the president decides whether to sign or veto the bill. Congress does not have enough votes to override a veto. Therefore, if the president vetoes the bill, the status quo remains $($i$.$e$.,$ neither A nor B become law$).$ Draw the game tree, making sure to label player's nodes and branches and payoffs, and indicate the equilibrium derived using backward induction.

b$)(5$ points$)$ Now suppose the rules of the game are changed in only one respect: the president is given the extra power of a line$-$item veto. Thus, if Congress passes a bill containing both A and B $,$ the president may choose not only to sign or veto the bill as a whole, but also to veto just one of the two items. Show the new game tree and equilibrium derived using backward induction.

c$)(5$ point$)$ In the case presented in $($b$)$ the president has more power. Generally speaking, people prefer more power to less. Considering only cases $($a$)$ and $($b$)$ above, is this true here? Explain why or why not; don't just refer to payoffs but the strategic implications of the line$-$item veto.