2. Consider the following dynamic game between players 1 and 2. Player one can chose two actions, L and R, and player two can chose, after observing player's one move, an action from {o, b, c, d}. In particular, player 2 can chose either a. or b after 1 picks L and either a or d after 1 picks R. Payoffs are as follows: if player 1 picks L, then she gets 0 and player 2 gets 10 if player 2 picks a, but she gets -3 and player 2 gets 2 if player 2 picks 5. Alternatively, player 1 gets 3 and player 2 gets 1 if player 1 picks R and player 2 pick 0, and player 1 gets -6 and player 2 gets -2 if player 1 picks R and player 2 pick d. a. Draw the extensiveform representation of this game. b. Is this a game of imperfect information; why? what are the information sets of each player? c. What are the strategies of these players? d. Write the normal-form representation of the game and nd all the pure NE. e. Are there NE that are not sequentially rational? If "yes", explain why. f. Find the Backward induction solution of the game. Is it sequentially rational? Why? g. Given the BI solution you found in e., what information sets are off-path? 3. Consider the following dynamic "penalty" game: 1 a. Is this a game of imperfect information; why? what are the information sets of each player? b. What are the strategies of these players