# For each of the games illustrated in Exercise U2, identify the rollback equilibrium outcome and the.

For each of the games illustrated in Exercise U2,
identify the rollback equilibrium outcome and the complete equilibrium strategy
for each player.

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Two distinct proposals, A and B, are being debated in
Washington. 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) The moves in the game are as follows. First, Congress
decides whether to pass a bill and whether the bill is to contain A or B or
both. Then the president decides whether to sign or veto the bill. Congress
does not have enough votes to override a veto. Draw a tree for this game and
find the rollback equilibrium.

(b) 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 tree and find the rollback equilibrium.

(c) Explain intuitively why the difference between the
two equilibria arises.