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

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.

Consider the following two player extensive form game. メ (2,5) (4,) (3,5) a. Find the induced normal form of the given extensive form game using the pure strategies of the players. Find out all the possible Nash Equilibrium of this game. b. From the Nash Equilibrium you are getting in part a., which one is subgame perfect Nash Equilibrium? Explain with appropriate reasons. c. Explain why the NE in part b. is credible. (Use maximum 3 sentences):

Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.

how many Nash equilibrium/equilibria are there in this game?  please refer to figure provided

The payoff matrix below shows the payoffs for Firm A and Firm B, each of whom can either "cooperate" or "cheat." The numbers in parentheses are (payoff for A, payoff for B). Firm B Cooperate Cooperate (30, 30) (x, 10) Cheat (10, X) (20, 20) Firm A Chent If x = 40, the Nash equilibrium is. O a. (Firm A: cheat, Firm B: cheat) O b. (Firm A: cooperate, Firm B: cheat) O c. (Firm A: cheat, Firm B: cooperate) O d. (Firm A: cooperate, Firm B: cooperate) O e. There is no Nash equilibrium for this value of x.

(b) ROWENA up Answer 1: up Answer 2: In this simultaneous move game, the iterated dominance equilibrium is (Rowena's . Colin's left left Answer 3: ). This game has two Nash equilibria one of which is the iterated dominance equilibrium. The other Nash equilibrium, which is not the IDE, is (Rowena's down Colin's right down Up Down Answer 4: Left right 0,0 0,0 COLIN Right 0,0 1,1

(a) Design a two-player game with the property that "the payoff for Player1 is Playerl plays a strategy Sl and Player2 plays a strategy S2 is the same as the payoff for Player2 if Player2 plays Sl and Playerl plays S2". Express your game in terms of payoff matrices. Show the above property holds in your given payoff matrices. Give a case to show that there is one Nash equilibrium and such an equilibrium is also a Pareto efficient (justify your answers) in your given payoff matrices. Prove or disprove the above case that is unique. Give another example to show that there are two Nash equilibria in your given payoff matrices.

Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.

1) Put together an example of a 2x2 game (two players with each having two options) that has NO pure-strategyNash equilibria. (Hint: just try some values and then change them as you need to; as an example think aboutthe Rock, Scissors paper which has no pure strategy NE).2) Using your own words, explain how the concept of elimination of dominated strategies differs from theconcept of Nash equilibrium.3) Indicate whether the following statement is TRUE or FALSE and explain your answer: If one player is theleader in a game it means that s/he has the first move in the game. The key thing is that this move can beobserved by the follower before making his/her own decision, otherwise it would be a simultaneous movegame that cannot be solved by backwards induction.4) MULTIPLE CHOICE (identify the one best answer below and explain your reasoning for each option): Recallthe Game of chicken from the previous problem set. If James is the leader in the game then: (hint: you candraw the game tree…