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

Problem 3. Consider the following two-player game. Player 1 (the row player) has three strategies {U, F, D}, and Player 2 (the column player) has four strategies {L, M, N, R}. In each cell, the first number is the pay-off of Player 1, and the second is that of Player 2. There is an unknown x in the table. Consider pure strategies only. U F D L (0, 3) (6,0) (3, 1) M (1,0) (5, 1) (4,2) N (2,5) (x, 2) (1, 1) R (4,2) (5, 1) (1, 3) (1) Find a number x such that {F, N} is the unique Nash equilibrium. (2) Find a number x such that the game has more than one Nash equilibria. What are these Nash equilibria in this case? (3) Is it possible to find a number x such that the game has no Nash equilibrium? For each of your answers above, an explanation needs to be provided.

Answer to image?

Q2 Consider a game between 2 payers (Ann and Bill) where each chooses between 3 actions (Up, Middle and Down). 1) Create a payoff matrix that reflects this. 2) Fill in payoff numbers that makes this game a Prisoner's Dilemma. 3) Explain why your game is a Prisoner's Dilemma.

Read-a-lot Bookstore and Frontier Books are competitors in the Carlton retail book market.  Each has a choice of setting a low price or high price.  The payoffs from the price choices are: Assume that the game is played sequentially with Frontier making a decision about its choice of price strategy, and then Read-a-lot, after observing Frontier’s strategy, chooses its price strategy. What is the best choice for Frontier?  [To answer this question, you need to take into account your answer for question 1 regarding the best strategy for Read-a-Lot.] a. Low price b. High price c. Frontier is indifferent between High price and Low price d. It is not possible to identify a best choice for Frontier.

Consider an example of the prisoner's dilemma where 2 firms are making sealed bids on a highway-construction contract and each firm is allowed to bid either $120 million or $130 million. If both firms bid the same price, the job is shared equally and each firm earns half the value of its bid. Otherwise the lowest bidder wins the contract and receives the full value of its bid (and the other bidder earns zero). The non-cooperative outcome in this situation is O A. both firms bid $130 million. B. one firm bids $120 million, the other firm bids $130 million. C. both firms bid $60 million. D. both firms bid $120 million. O E. both firms bid $65 million. OO

What is the difference between 'grim trigger' and 'tit-for-tat' in the context of the repeated prisoner's dilemma? Tit-for-tat requires players to consider the entire history of past play when making their choice. Grim trigger is able to achieve cooperation in some cases where Tit-for-Tat cannot. Grim trigger allows players to achieve the cooperative payoff. Grim trigger is more forgiving and allows for occasional defection. Tit-for-tat only defects after the opponent defects. No Answer

Please solve the following problem using a game theory. Consider a scenario in which two companies, Company A and Company B, are competing for a government contract to supply a specific product. The government has set a maximum budget for the contract, and both companies want to maximize their profits. However, the government will only award the contract to the company with the lowest bid, and the companies have to submit sealed bids simultaneously. Company A and Company B both have two options: bid high or bid low. If both companies bid low, they will share the contract and split the profits equally. If one company bids low and the other bids high, the company bidding low will win the entire contract and maximize its profits, while the other company will receive nothing. If both companies bid high, neither will win the contract, and they will receive no profits. The profit structure is as follows (in millions of dollars): If both companies bid low: Company A gets $10 million, and…

Consider a modification of driving conventions, shown in the figure below, in which each player has a third strategy: to zigzag on the road. Suppose that if a player chooses zigzag, the chances of an accident are the same whether the other player drives on the left, drives on the right, or zigzags as well. Let that payoff be 0, so that it lies between –1, the payoff when a collision occurs for sure, and 1, the payoff when a collision does not occur. Find all Nash equilibria.

Consider the signaling game below. Does the game have a perfect Bayesian equilibrium in which all sender types play L? Does there exist a perfect Bayesian equilibrium in which all sender types play R? Explain. 1,1 1,00 2,1 0,0 0,0 14 Receiver u Receiver 14 L L L (1/3) 1₂ R (1/3) R (1/3) R 14 Receiver 14 Receiver U 0,1 0,0 1,1 1,0 0,0 2,1