Use the following normal-form game to answer the questions below. Player 1 Strategy A B a. Identify the one-shot Nash equilibrium. O (A,D) Player 2 C D 20, 20 5, 50 50, 5 35, 35 O (B,C) O (B,D) O (A,C) b. Suppose the players know this game will be repeated exactly three times. Can they achieve payoffs that are better than the one- shot Nash equilibrium? O No O Yes c. Suppose this game is infinitely repeated and the interest rate is 5 percent. Can the players achieve payoffs that are better than the one-shot Nash equilibrium? ○ Yes O No

Consider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.

Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium.                                         Firm 2                                 Launch       Don’tFirm 1      Launch     60, -10      100, 0                  Don’t       80, 30      120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.

2- Consider the following game. Player 2 Player 1 U 12, 2 | 3, 9 5, 8 4, 2 D (a) Find all the Nash equilibria, pure and mixed. (b) Suppose that the payoff of the column player u:(D, L) is reduced from 8 to 6, but all other payoffs remain the same. Again, find all the pure- and mixed-strategy Nash equilibria. (c) Compare the mixed-strategy equilibria in parts (a) and (b). Did this worsening in one of player 2's payoffs change player 2's equilibrium mixed strategy? Did it change player l's? Give some intuition.