Two players must choose among a pool of three candidates: {a; b; c}. Player 1 prefers a to b and b to c. Player 2 prefers b to a and a to c. The rules are that player 1 moves first and can veto one of the three candidates. Then player 2 can choose one of the remaining two candidates.

(a) Draw the game tree that represents this game assuming that a player's most preferred candidate gives a payoff of 2, the second-most preferred candidate gives a payoff of 1, and the least preferred candidate gives a payoff of 0.

(b) How many pure strategies does each player have?

(c) Find the SPNE(Subgame Perfect Nash Equilibrium). Is it unique?

(d) Are there NE(Nash equilibrium) that are not SPNE?