There are three players in this simultaneous move game. Player-3 chooses between game A and game B. Player-1 chooses between U, M and D. Player-2 chooses between L and R. The payoffs are given below: P-1 U M D L 5,5,0 6,4,5 3,1,2 A P-2 R 1,4,0 2,5,3 3,3,1 Find all pure strategy N.E. of this game. P-1 U M D L 4,8,0 4,1,3 3,5,1 B P-2 R 2,1,0 3,3,3 0,3,0

one two X, 14 three four Firm B Low Firm A Sell High 6, Y Buy Low Let X = 9, Y = 15 and Z=10. This game has 10, Z Firm B High 8,8 Nash equilibrium.

2. For the following payoff matrix find all of the mixed strategy Nash equilibria (check for dominated strategies to eliminate). Player 1 X Y Z A 1,3 4,1 2,3 Player 2 B 2,4 3,1 0,0 C 2,3 5,0 4,2

For the game below, find all mixed-strategy Nash equilibria.

Team 2 plays A Team 2 plays B Team 2 plays C Team 1 plays A 9, 9 8, 12 6, 6 Team 1 plays B 6, 6 0, 7 5, 5 Team 1 plays C 12, 8 10, 10 7,0 Consider the simultaneous move game above in which two teams are competing against each other. Which of the following statements are true? In all Nash Equilibria of the game Team 2 plays B This game has two Nash Equilibria Team 1's best response to team 2 playing B is to play A. O None of the other answers are correct This game has a mixed strategy Nash Equilibria where a player randomizes over multiple options.

Consider a simultaneous game where player A has a dominant strategy and player B has two strategies (none of which is a dominant strategy). How many pure strategy Nash equilibria will this game have? A) Exactly 1 B) Exactly 2 C) Either 1 or 2 D) None

Player 1 3 Up 0 Down Player 2 Left 4,38 0,0 Right -1,-1 Refer to the payoff matrix above. How many Nash Equilibriums this game has? 01 3,4

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…

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

Consider the following game:   Sarah R S T   Peter    X 9, 6 4, 4 6, -3 Y 6, 6 7, 6 2, 2 Z 9, 7 1, 5 6, 7   How many (pure strategy) Nash equilibria does this game have?