1. Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs: Firm B - low output Firm B - high output Firm A - low output 300, 250 200, 100 Firm A - high output 200, 75 75, 100 a. Draw a tree (extensive form) of this game. b. Describe what is meant by a dominant strategy. c. Given the payoff matrix above, does each firm have a dominant strategy? What are the dominant strategies in this game? d. What is the Pure Strategy Nash Equilibrium for this game?2. Consider the following 3-player game where each player has 3 strategies. Player 1 decides up, middle, or down (U, M, D). Player 2 simultaneously decides whether to go left, center, or right (L, C, R). Player 3 decides whether to move forward, backward, or stay put (F, B, S). Using the payoffs shown below, nd all Pure Strategy Nash Equilibrium. \\ L c R L C R L c l R U ' 2,1,3 2,2,2 2,1,3 3,3,4 4,1,1 6,2,3 4,2,2 2,1,3 ' 3,3,3 M ' 3,2,2 3,1,2 4,2,5 1,3,2 4,2,2 4,1,5 2,1,1 1,1,1 ' 3,4,1 D ' 2,1,1 1,2,3 4,1,3 9,1,1 2,1,1 3,0,3 3,4,5 3,7,1 ' 4,4,3 F B S 3. Consider the game below: a. What are the dominant strategies in this game? b. What is the Pure Strategy Nash equilibrium for this game? c. Find all Mixed Strategy Nash Equilibrium. 4. Consider the game below: ' Woman - Football Woman - Shopping Man Football 4, 3 2, 2 Find all Pure and Mixed Strategy Nash Equilibrium