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