Perfect and Imperfect Recall: Consider the game depicted in Figure 7.14.
a. What are the pure-strategy sets for each player?
b. Show that for any behavioral strategy for player 1 there is a mixed strategy that leads to the same distribution over the terminal nodes regardless of the strategy chosen by player 2.
c. Show that for any behavioral strategy for player 2 there is a mixed strategy that leads to the same distribution over the terminal nodes regardless of the strategy chosen by player 1.
d. Now imagine that the game does not have perfect recall so that player 2's bottom two information sets are now one large information set. Can you find an example showing that the claim in (c) is no longer true?
