📗 The quizzes must be completed during the lectures and submitted on TopHat: Link. No Canvas submissions are required. The grades will be updated by the end of the week on Canvas.
📗 Please submit a regrade request if (i) you missed a few questions because you are late or have to leave during the lecture; (ii) you selected obviously incorrect answers by mistake (one or two of these shouldn't affect your grade): Link
The following questions may appear as quiz questions during the lecture. If the questions are not generated correctly, try refresh the page using the button at the top left corner.
📗 [4 points] Perform iterated elimination of strictly dominated strategies (i.e. find rationalizable actions). Player A's strategies are the rows. The two numbers are (A, B)'s payoffs, respectively. Recall each player wants to maximize their own payoff. Enter the payoff pair that survives the process. If there are more than one rationalizable action, enter the pair that leads to the largest payoff for player A.
A \ B
I
II
III
I
II
III
IV
📗 Answer (comma separated vector): .
📗 [4 points] What is the row player's value in a Nash equilibrium of the following zero-sum normal form game? A (row) is the max player, B (col) is the min player. If there are multiple Nash equilibria, use the one with the largest value (to the max player).
A \ B
I
II
III
IV
I
II
III
IV
📗 Answer: .
📗 [4 points] Given the following BoS (Battle of Sexes) game, what is the row (Romeo) player's (expected) value (i.e. payoff) in the mixed strategy Nash equilibrium?
Romeo \ Juliet
Bach
Stravinsky
Bach
Stravinsky
📗 Answer: .
📗 [4 points] Given the following game payoff table, suppose the row player uses a pure strategy, and column player uses a mixed strategy playing L with probability \(q\). What is the smallest and largest value of \(q\) in a mixed strategy Nash equilibrium?
Row \ Col
L
R
U
D
Note: the following is a diagram of the best responses (make sure you understand what they are and how to draw them). The red curve is the best response for the column player and the blue curve is the best response for the row player.