Consider a game in which there are two players, A and B. Player A moves first and chooses either Up or Down. If A chooses Up, the game is over, and each player gets a payoff of 2. If A moves Down,...

Consider a game in which there are two players, A and B. Player A moves first and chooses either Up or Down. If A chooses Up, the game is over, and each player gets a payoff of 2. If A moves Down, then B gets a turn and chooses between Left and Right. If B chooses Left, both players get 0; if B chooses Right, A gets 3 and B gets 1.

(a) Draw the tree for this game, and find the subgame-perfect equilibrium.

(b) Show this sequential-play game in strategic form, and find all of the Nash equilibria. Which is or are subgame-perfect? Which is or are not? If any are not, explain why.

(c) What method of solution could be used to find the subgame-perfect equilibrium from the strategic form of the game?