Question

1. Suppose you email your professor to ask an appointment to discuss your midterm grade. The professor answers you to stop by his office at 3pm the next day. At this point,

A. It is now common knowledge that you and your professor will meet tomorrow.

B. It is not common knowledge that you will meet tomorrow.

C. It may or may not be common knowledge depending on whether player are rational and self-interested

D. It is not common knowledge that you will meet tomorrow because your email exchange is private between you and professor.

2. How many strategies does each of player 1 and player 2 have? At how many information sets does player 2 move?

Consider a game in which player 1 moves first. The set of actions available to player 1 is A₁={A,B,C}.

After observing the choice of player 1, player 2 moves. The set of actions available to player 2 is A₂={a,b,c,d}.

Answer 1

Answer (1): Common Knowledge in a Game theory refers to a situation in understanding among the players in the game where both the players (or the total number of players) in the game are mutually aware of a fact or condition. In the give situation, where we have sent an email to the Professor and asked for an appointment to discuss the grade achieved in the midterm, and the Professor has advised back or replied to stop by his office the next day. If we assume both these individuals to be the two players in a game, then both the players in the game are aware of the fact that both the parties or players would meet tomorrow. Therefore, the correct answer would be A. It is now common knowledge that you and your professor will meet tomorrow.

Answer (2)

Player 1 (The Student) has the following strategies :

1. The Player 1 accepts the invitation of the Player 2 to meet the following day.
2. The Player 1 rejects the invitation of the Player 2 to meet the following day.
3. The Player 1 accepts the invitation of the Player 2 to meet, but not the following day and replied to discuss and change and set a different meeting slot.
4. The Player 1 does not appear for the meeting even after accepting the invite.

Player 2 (The Professor) has the following strategies :

(Note: The Professor has already accepted the proposal of the student and proposed a meeting time and place)

1. The Player 2 re-writes another email to Player 1 rejecting his request for a discussion.
2. The Player 2 re-writes another email to Player 1 accepting his request for a discussion , but changes the slot and time of the meeting.
3. The Player 2 accepts the discussion but us never available for the meeting

Since, The Set of Actions available for Player 1 is A1=(A,B,C) and he can choose any of the three actions , therefore if the Player 1 moves option A , player 2 will also move Option A to meet . Similarly, if Player 1 moves the option B, then player 2 may choose option C and re-ask the player 1 to change his decision.