I was asked this question in an interview: There are two people Mike and Cheng with one blank card each. Both write either a '0' or a '1' on it without showing the other while writing. They then simultaneously show their cards to each other. If the payoffs are as follows depending on the cards shown:
1,1: Mike pays Cheng 3
0,0: Mike pays Cheng 1
1,0: Mike receives 2 from Cheng
0,1: Mike receives 2 from Cheng
Is this game fair?
Using game theory I reason: Cheng will always play 1 because his payoff from 1 is (-2 or 3) as opposed to his payoff from playing 0 which is (1 or -2). Knowing that Cheng will prefer to play 1, Mike always plays 0 to get a payoff of 2. So the game is unfair to Cheng.
But I also reason: Mike will never play 1 because he has a payoff (2 or -3) vs playing 0 which has a payoff (-1 or 2). So Mike will always prefer to play 0 (this is also inline with the above reasoning). Knowing that Mike will always prefer 0, Cheng always plays 0 so Mike gets -1 every round. So this game is unfair to Mike.
Regardless if the game is played one round or many rounds, I am unable to conclude which is correct.
Can anyone help explain why I am getting conflicting results?
PS: Later the interviewer told me that the game is unfair and Mike always wins.
PPS: I apologize in advance if I have made any mistakes in the posting - this is my first post.