Warm-Up 2, Due Monday, January 28, 12:00 noon.

Warm-up questions usually either address material we handled during last class, or material you were to read in preparation for class, or you are supposed to answer questions based on your common sense alone. Please answer each question in three or more sentences. It is OK to answer 'I don't know' - but try to tell me why you are confused! No late Warm Ups are accepted for any reason, and only those submitted electronically through this web page (or by email, if the web page has technical problems) are considered.

Your Name:

Consider the following simultaneous game: Two players, Ann and Beth, have three cards of value 1, 2, or 3 in their hands. Both put one card face down on the desk. Then the cards are revealed, and according to the outcome, the following payoffs are payed:

If both did put the same card down, then both get as many CHFs as the card shows.
If one played "1" and the other player "2", then the one playing "1" gets one CHF and the other 2 CHFs.
If one played "1" and the other player "3", then the one playing "1" gets 3 CHFs and the other 100 CHFs. (yes, one hundred CHF!)
If one played "2" and the other player "3", then the one playing "2" gets 4 CHFs and the other 3 CHFs.

Question 1

Is the game a zero-sum game? Give a reason.

Question 2

Type in the bimatrix of the game.

Question 3

Consider the following two-player game with players Ann and Beth, where Ann has three choices, A1, A2, or A3, and Beth has also three choices, B1, B2, B3.

B1 B2 B3

A1 1, 7 2, 9 1, 8

A2 1, 2 4, 3 1, 1

A3 2, 5 3, 8 2, 6

What is the payoff for Beth if Ann plays A2 and Beth plays B1? And overall---do you think this game is fair? If not, who will have an advantage?