Question

Alexander and Eliza are playing a sequential game of perfect information.

Alexander moves first and he chooses between Up and Down. If Alexander chooses Up, it is Eliza’s turn and she chooses between Left and Right. If Eliza chooses Left (after Alexander chose Up) the game ends and Alexander gets a payoff of 4 whereas Eliza gets a payoff of 3. If Eliza chooses Right (after Alexander chose Up), then it is Alexander’s turn again and he chooses between In and Out. If he chooses In (after Alexander chose Up in the first period and Eliza choose Right) the game ends, Alexander gets 7 and Eliza gets 2. If he chooses Out (after Alexander chose Up and Eliza choose Right) the game ends, Alexander gets 6 and Eliza gets 8.

If Alexander chose Down (at the very begining of the game), it is Eliza’s turn and she chooses between Left and Right. If Eliza chooses Left (after Alexander chose Down) the game ends and Alexander gets a payoff of 6 whereas Eliza gets a payoff of 3. If Eliza chooses Right (after Alexander chose Down), the game ends and Alexander gets a payoff of 2 whereas Eliza gets a payoff of 5.

a) Draw the extensive form representation of this game.

b) Write down the strategy sets of Alexander and Eliza.

c) Find all subgame perfect Nash equilibria of this game. Explain which method you are using 1 when finding the subgame perfect Nash equilibria. Show and explain every step of your reasoning.

Answer 1