Two legislators select a policy that affects them both, by alternately vetoing policies until one remains. First legislator 1 vetoes a policy. If more than one policy remains then legislator 2 vetoes a policy. If more than one policy still remains, legislator 1 then vetoes another policy. The process continues until a single policy remains unvetoed.

(a) Suppose there are three possible policies, A, B, and C. Suppose furthermore that legislator 1 prefers A to B to C, and legislator 2 prefers C to B to A. Draw the game tree and identify the subgame perfect equilibria of the game. List all the available strategies of the two players.

(b) Find the Nash equilibria of the game in part (a). What is the relationship between the subgame perfect equilibria and the Nash equilibria? Verify your answer.

(c) Now suppose that there are four possible policies instead of three, namely A, B, C, and D. Suppose furthermore that legislator 1 prefers A to B to C to D, and legislator 2 prefers D to C to B to A. Identify the subgame perfect equilibria of this game