1. Consider the zero-sum game given by 3 1 2 A = 4 0 2 1 2 -2 3 1 (a) Calculate the gain floor and loss ceiling for A. (b) Without using dominance, use the Equilibrium Theorem to determine whether it is possible for A to have a mixed Nash Equilibrium where player two's strategy is of the form (a, b, c, 0) with a, b, c > 0.

Consider the following sequential game: 1 O D,L U.L U,R U D,R D (0,2) 2 L What is the subgame perfect Nash equilibrium of this game? R. (-1,-1) (1,1)

Use the following payoff matrix for a one-shot game to answer the accompanying questions.         Player 2       Strategy  X Y Player 1  A      30, 30              16, -50 B     -50, 16        50, 50 A. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication.  check all that apply (16, −50) (−50, 16) (30, 30) (50, 50) Which of these outcomes would you consider most likely? multiple choice (16, −50) (50, 50) (−50, 16) (30, 30) B. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter? multiple choice  A or B What outcome do you think would occur as a result? multiple choice  (−50, 16) (16, −50) (30, 30) (50, 50) c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move structure is…

Consider the following game:

1.9. What is a mixed strategy in a normal-form game? What is a mixed-strategy Nash equilibrium in a normal-form game?