2. Turning a verbal description into a 2x2 game matrix. In class I mentioned the Bonk Test. Here's a related one-question exam and a game it generates. Suppose there are only two students in the class, Sandy and Pat. They receive this exam question, which they have to answer separately, and also they receive this grading scheme:

Question: Write down either the word "Red" or "Blue."

Grading: - If both of you choose Blue, both get B+. - If Sandy chooses Red and Pat chooses Blue, Sandy gets A, and Pat gets C. - If Sandy chooses Blue and Pat chooses Red, it's C for Sandy and A for Pat. - If both of you choose Red, both get B-.

(a) Write down a game matrix with labels of the players and their two moves in the right places. Make Sandy the row chooser and Pat the column chooser. Make Red each one's first move and Blue each one's second move. In the cells put the outcomes A, B+, B- and C. You'll put a pair of outcomes in the cell, the first for Sandy and the second for Pat.

(b) Write down a second game matrix where the cells contain pairs of values for the players of each outcome. Each values A as 4, B+ as 3.3, B- as 2.7 and C as 2.

(c) A basic question to ask about a game is whether a player has a move that's best no matter what the other players does. Does Sandy or both have a best move no matter what the other does? In that case, in deciding their own moves they don't need to consider the other's viewpoint on the game. Or is this game like Rock, Paper and Scissors, where one player's best move changes depending on the move that the other uses?