Suppose there are two competing bills: A and B; and three legislators (voters): 1, 2, and...

Suppose there are two competing bills: A and B; and three legislators (voters): 1, 2, and 3. After all the voting takes place, three things can happen: bill A is passed, bill B is passed, or no bill is passed. The voting procedure is as follows:

1. In the first round legislators simultaneously (in a sealed envelope) vote for either bill A or B and the bill with the majority of the votes wins.

2. Then, the winner of the first round (either A or B) is voted against the status quo: no bill (that we will denote by N). This second-stage voting is simultaneous (in a sealed envelope) and the winner is selected by majority. After this second round the game ends in one of the three ways listed above.

Suppose legislators have the following preferences Voter 1: A > N > B.

2: B > A > N

3: N > A > B

(a) Apply IEDS to simplify the game (Hint: note that voting truthfully is a dominant strategy in the second round for every voter)

(b) Find a Subgame Perfect Nash equilibrium (SPNE) in which players do not play dominated strategies.

(c) Are there SPNE in which players play dominated strategies?

Expert Solution

Rahul Sunny answered 2 years ago

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