Problem Set $1$

Remember to show your work! Correct answers will not receive full credit unless there is sufficient work to demonstrate how they were reached. Similarly, wrong answers with correct work will receive partial credit.

$(25$ pts$)($a$)$ Represent the following game in the extensive form. There are three players:

A diplomat can choose to summon a terrorist his country is sponsoring to a meeting, or not. If he does not, an undercover CIA officer can choose to impersonate him and summon the terrorist to a meeting, or not. If summoned the terrorist does not know who summoned him and can choose to go to the meeting, or not. If the terrorist attends the meeting, and the diplomat summoned him, he and the diplomat get $6,$ and the officer gets $0.$ If he does not attend the meeting and the diplomat summoned him, he gets $-6,$ the diplomat gets $0,$ and the officer gets $0.$ If the terrorist attends the meeting, and the officer summoned him, he gets $-6,$ the diplomat gets $-1,$ and the officer gets $6.$ If the terrorist does not attend the meeting, and the undercover officer summoned him, he gets $6,$ the diplomat gets $6,$ and the officer gets $0.$ If there is no summons and no meeting, all players get $1.$

$($b$)$ Suppose the game above is instead structured so that the terrorist knows whether it was the undercover officer or the diplomat who summoned him to the meeting. List the strategy set for each player.

$(25$ pts$)$ Convert the following normal form games to extensive form games. Note an alternative way to convert each normal form game to an extensive form.

$($a$)$