Two players, Player 1 and Player 2, are playing a repeated prisoner’s dilemma. Payoffs are described in the following matrix. Answer which statement is correct: Select one: a. A trigger strategy will never support (A,A) as an equilibrium b. A tit-for-tat strategy will never support (A,A) as an equilibrium c. A tit-for-tat strategy will support (A,A) as an equilibrium if δ > 0.7 d. A trigger strategy will support (A,A) as an equilibrium if δ > 0.7
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Two players, Player 1 and Player 2, are playing a repeated prisoner’s dilemma. Payoffs are described in the following matrix. Answer which statement is correct:
Select one:
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- 1) Suppose that Player A can take two actions, either Up or Down. Player A is thinking to choose Up 50 percent of the time, and Down 50 percent of the time. This type of strategy is called a ____ ? 2) Consider a payoff matrix of a game shown below. In each cell, the number on the left is a payoff for Player A and the number on the right is a payoff for Player B. In order for (Down, Right) to be a unique pure strategy Nash equilibrium, a must be (greater, or smaller) than 3 and b must be (greater, or smaller) than 3. refer to imageA strategy is a decision rule that describes the actions a player will take at each decision point. The normal-form game indicates the players in the game, the possible strategies of the players, and the payoffs to the players that will result from alternative strategies. In the game presented in Table Normal-Form Game, does player B have a dominant strategy? What is the secure strategy for player B in the game presented in Table Normal-Form Game?A payoff matrix is shown below. With the payoffs in each field indicated in the form (Player 1’s payoff, Player 2’s payoff). Player 2 Left Right Player 1 Up ($1, $1) ($2, $4) Down ($7, $8) ($3, $3) Which of the following is true? The only Nash Equilibrium is Player 1 playing ‘Up’ and Player 2 playing ‘Right’. The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Left’. The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Right’. None of the other answers provided are true.
- The following payoff matrix represents a simultaneous-move game between two players: John and Trevor. Each player has to choices: Black or White. The first number in each cell is the payoff to John, and the second number is the payoff to Trevor. Trevor Black White Black 15, 15 10, 10 John White 12, 10 13, 15 Refer to the table above. Which statement is true? a. Neither John nor Trevor have a dominant strategy in this game. b. Only Trevor has a dominant strategy in this game. c. Only John has a dominant strategy in this game. d. John and Trevor both have a dominant strategy in this game.Let’s say there are two friends, Adam and Jason who each has two strategies: Share and don’t share notes to classmates a night before final exam. The payoff for each of them is in the above payoff matrix. a) Do you think this game has a dominated strategy equilibrium? Is it a stable equilibrium? Justify your answer. b) Is it worth for both of them to end up sharing notes to others a night before final exam? Justify your answer.Consider the R&D game being played by Huawei and Samsung. Huawei can choose to develop a new camera for its phone (C) or not (N). Samsung observes the choice of Huawei, then can make its own choice of C or N. The payoffs are as follows. If Huawei opted for C and Samsung likewise chose C, the payoffs are (100, 80) for Huawei and Samsung, respectively. If the choices are C by Huawei and N for Samsung, the payoffs are (120, 60). If Huawei opts for N and Samsung C, the payoffs that ensue are (80 120). If Huawei chooses N and Samsung N the payoffs are (140, 100). Which of the following statements are true? N by Samsung following N by Huawei is a credible strategy for Samsung C by Samsung following C by Huawei is a credible strategy for Samsung N by Samsung following C by Huawei is a credible strategy for Samsung C is a dominant strategy for Samsung N is a dominant strategy for Samsung
- A and B are competitors in the mobile phone industry. Both A and B have to decide whether to participate or not to participate in a Phone for the Future Trade Fair next month. The matrix payoff below shows the profits (USD million) corresponding to their actions. a) What is the Nash equilibrium of the above game? b) Is the Nash equilibrium Pareto Optima? Explain. c) Suppose B is pessimistic of A's rationality, what is B's strategy? Compare and comment on B's strategy in (a) and (c). A Participate Do not participate B Participate Do not participate 400,1000 200,200 500,500 1000,400Suppose that you and a friend play a matching pennies game in which each of you uncovers a penny. If both pennies show heads or both show tails, you keep both. If one shows heads and the other shows tails, your friend keeps them. Show the pay- off matrix. What, if any, is the pure-strategy Nash equilibrium to this game? Is there a mixed-strategy Nash equilibrium? If so, what is it?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), Player 2’s choices are shown in the column headings (C/D). The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 C D A 8, 3 2, 4 B 7, 4 3, 5 Pick 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 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 The Nash equilibrium outcome to this game is: A/C A/D B/C B/D There is no pure strategy Nash equilibrium for this game
- Question 1 Consider the following game. Player 1 has 3 actions (Top, middle,Bottom) and player 2 has three actions (Left, Middle, Right). Each player chooses their action simultaneously. The game is played only once. The first element of the payoff vector is player 1’s payoff. Note that one of the payoffs to player 2 has been omitted (denoted by x). A) Suppose that the value of x is such that player 2 has a strictly dominant strategy. Find the solution to the game. What solution concept did you use to solve the game? B) Suppose that the value of x is such the player 2 does NOT have a strictly dominant strategy. Find the solution to the game. What solution concept did you use to solve the game?Use the following payoff matrix to answer the questions below. Cooperate Defect 1 Cooperate 100, 100 40, 125 Defect 125, 40 50, 50 Which player (if any) has a Dominant Strategy? [ Select ] What is the Nash Equilibrium of this game? [ Select ] Does this game satisfy the definition of a prisoner's dilemma? [ Select ]Consider a game where player A moves first, choosing between Left and Right. Then, after observing player A’s choice, player B moves next choosing between Up and Down. Which of the following is true? This is a game where players A and B have the same number of strategies. Player A will get a higher payoff than player B as A moves first. This is game will only have one Nash equilibrium. This is a game of perfect information.