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 among Left and Right. If B chooses Left, both players get 0; if B chooses Right, A gets 3 and B gets 1.
1. Draw the tree for this game, and discover the sub game-perfect equilibrium.
2. Show this sequential-play game in strategic form, and find all of the Nash equilibrium. Which is or are sub game-perfect? Which is or are not? If any are not, describe why.
What method of solution could be used to discover the sub game-perfect equilibrium from the strategic form of the game?