# Sequential-form game (game tree diagram)

• Oct 5th 2008, 06:51 PM
truxmonster
Sequential-form game (game tree diagram)
Assume that we can treat Congress as a unitary rational actor and assume that Congress cannot override Presidential vetos. Suppose Congress is debating two distinct policy proposals, A and B. Congress would be happiest if it could enact A alone. Congress would rather enact policies A and B together than enact nothing, but it would rather enacy nothing than enact B alone. The President, on the other hand, would be happiest if he could enact B alone. He would rather enact policies A and B together rhan enact nothing, but he would rather enact nothing than enact A alone.

(a) We can represent the present system for adopting legislation as a sequential-form game. Congress moves first by proposing a law to the President. Congress has four possible actions: A, B, both, or no change (N). For any proposal that Congress makes, the President decides whether to accept (sign) or reject (veto) the entire bill. Draw the game and solve it by backwards induction.

What I have for this problem right now are the preferences...

Congress: A>AB>N>B
President: B>AB>N>A

I've drawn the tree, but can you show me how to pick the outcome probablities?

The examples that my professor has shown in class include the outcomes so I'm not very sure how to solve a problem without them.