A professor plays a simplified poker game with one of

A professor plays a simplified poker game with one of his students. The rules are as follows. The student and the professor each put $1 in a pot. The professor randomly draws a card from a deck of cards that consists of 4 kings and 4 queens. The professor looks at the card that he drew but does not show it to the student. The professor then must either “fold” or “bet”. If the professor folds, the game ends and all of the money in the pot goes to the student, so the professor loses $1 and the student wins $1. If the professor bets, then he must put another dollar in the pot. In this case, the student must decide whether to fold or bet. If the student folds, the game ends and all of the money in the pot goes to the professor. If the student bets, she must add another dollar to the pot and then the professor must show the card that he has drawn. If the card is a king, the professor gets all of the money that is in the pot. If the card is a queen, the student gets all of the money in the pot.

A) Is this a constant sum game?

B) Show this game in extensive form.

C) How many strategies are possible for the professor? How many for the student?

D) Show this game in strategic form.

E) How many pure strategy Nash equilibria does this game have?