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- Player 1 X Y Player 2 1 2 1 3,2 2 Wo 1 1,3 -0,1 hich of the following is the Subgame Perfect Nash Equilbrium in thisA game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?Use the following payoff matrix for a one-shot game to answer the accompanying questions. Player 2 Strategy X Y Player 1 A 50, 50 -110, 6 B 6, -110 26, 26 a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication.check all that apply (26,26) (50,50) (-110,6) (6,-110) Which of these outcomes would you consider most likely?multiple choice 1 (-110,6) (50,50) (6,-110) (26,26) 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 2 B A What outcome do you think would occur as a result?multiple choice 3 (26,26) (50,50) (-110,6) (6,-110) 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…
- 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…In the game presented in Table, what are the Nash equilibrium strategies for players A and B?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
- Use the following normal-form game to answer the questions below. Player 2 Strategy C D Player 1 A 50, 50 120, 25 B 25, 120 55, 55 a. Identify the one-shot Nash equilibrium.multiple choice 1 (B,C) (B,D) (A,C) (A,D) 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?multiple choice 2 No Yes c. Suppose this game is infinitely repeated and the interest rate is 6 percent. Can the players achieve payoffs that are better than the one-shot Nash equilibrium?multiple choice 3 No Yes d. Suppose the players do not know exactly how many times this game will be repeated, but they do know that the probability the game will end after a given play is θ. If θ is sufficiently low, can players earn more than they could in the one-shot Nash equilibrium?multiple choice 4 Yes Noif Y =4 (b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 7 7, 2 2, 6 B 5, 5 5, 4 8, 4 C 4, 6 8, 4 7, 5 D 1, 6 3, 5 6, 4 Highlight the correct answer: Player 1: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy Player 2: Has a dominant strategy to choose E Has a dominant strategy to choose F Has a dominant strategy to choose G Does not have a dominant strategy The Nash equilibrium outcome to this game is: A/F B/E B/G C/F C/G There is no pure strategy Nash…
- Consider the following game. Which one of the following statements is TRUE? 1. There are 8 subgames for this extensive-form game. 2. There are 8 proper subgames for this extensive-form game. 3. There is no Subgame Nash Equilibrium for this game. 4. There exists some Subgame Nash Equilibrium that gives the payoff 7 to Player 1 and 3 to Player 2.Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 4 7, 7 2, 6 B 10, 6 1, 7 12, 4 C 4, 6 8, 8 7, 7 D 1, 6 3, 9 6, 7Consider the following game. There are two payers, Player 1 and Player 2. Player 1 chooses a row (10, 20, or 30), and Player 2 chooses a column (10/20/30). Payoffs are in the cells of the table, with those on the left going to Player 1 and those on the right going to player 2. For example, a payoff 100/200 would mean Player 1 receives 100 and Player 2 receives 200.What is [are] the Nash Equilibrium [Equilibria] of this game?A) (10/10) and (20/20)B) (30/30)C) (10/20) and (20/10)D) (20/20)E) (30/30)