1. Consider a game of two players. The following information is common knowledge between the two players. First, Lisa chooses between actions u and d. Then, Sam observes which action Lisa has chosen with probability 1/3. With probability 2/3, he does not observe the action Lisa has chosen. (Hence, at the time Lisa makes her decision, she does not know whether Sam will observe or will not observe her choice. She believes that with probability 1=3, her choice will be revealed to Sam, and with probability 2=3, her choice will not be revealed to Sam.) Regardless of whether Sam has observed that Lisa chose u, or he has observed that Lisa chose d, or he has not observed any action, Sam chooses between actions l and r. The payoff of each player is 1 after (u; l) and (d; r), and 0 otherwise.

(a) Write the above game in extensive form.

(b) Write the above game in normal form.