Exercise 4. Consider a simplified model of voting in a Senate committee. The committee has three members (A,B,C), the first two are Republicans and the last a Democrat. The committe considers two versions of a bill to restructure welfare. Bill 1 a modest adjustment, while bill 2 is much more radical. The committee votes between the two bills, and whichever gets a majority in committee is recommended to the full senate chamber. The full senate then votes simultaneously along party lines between the status quo and the committee recommendation. If a majority of the sentate votes in favor, the bill passes; otherwise we keep the status quo. Senators of the two parties have the following preferences: - Democrats: bill 1 status quo bill 2 - Republicans: bill 2 bill 1 status quo Answer the following: - Represent this as an extensive form game (model each senator in committee, but just the two parties in the full senate). - Identify all subgames. - How do the senators vote in the second stage, if no one plays a weakly dominated strategy? - Suppose there is a Democratic senate majority. Find the subgame perfect Nash equilibrium. What if there is a Republican senate majority? Exercise 4. Consider a simplified model of voting in a Senate committee. The committee has three members (A,B,C), the first two are Republicans and the last a Democrat. The committe considers two versions of a bill to restructure welfare. Bill 1 a modest adjustment, while bill 2 is much more radical. The committee votes between the two bills, and whichever gets a majority in committee is recommended to the full senate chamber. The full senate then votes simultaneously along party lines between the status quo and the committee recommendation. If a majority of the sentate votes in favor, the bill passes; otherwise we keep the status quo. Senators of the two parties have the following preferences: - Democrats: bill 1 status quo bill 2 - Republicans: bill 2 bill 1 status quo Answer the following: - Represent this as an extensive form game (model each senator in committee, but just the two parties in the full senate). - Identify all subgames. - How do the senators vote in the second stage, if no one plays a weakly dominated strategy? - Suppose there is a Democratic senate majority. Find the subgame perfect Nash equilibrium. What if there is a Republican senate majority