9.In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player 2 is described as follows:⚫ There are two "statuses" that player i might be in during any period: "normal" and "revenge";•In a normal status player i cooperates;⚫ In a revenge status player i defects;• From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period;• From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player's action in thisperiod.Consider an infinitely repeated game so that with probability p that the game continues to the next period and with probability (1-p) it ends.Cooperate (C)Defect (D)Cooperate (C)4,45,0Defect (D)0,51,1What is the threshold p* such that when p≥ p* always cooperating by player 2 is a best response to player 1 playing tit for tat and starting in anormal status, but when p < p* always cooperating is not a best response?◇ a) 1/2○ b) 1/3○ c) 1/4○ d) 1/5

The Prisoner's Dilemma and Tit-for-Tat: Finding the Threshold for CooperationThe Prisoner's Dilemma…

Answered: 9. In an infinitely repeated Prisoner's…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter13: best-practice Tactics: Game Theory

Section: Chapter Questions

Problem 2E

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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). 1. Determine the range of values for x such that Player 2 has a strictly dominant strategy.
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?
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 image
Consider the following game - one card is dealt to player 1 ( the sender) from a standard deck of playing cards. The card may either be red (heart or diamond) or black (spades or clubs). Player 1 observes her card, but player 2 (the receiver) does not - Player 1 decides to Play (P) or Not Play (N). If player 1 chooses not to play, then the game ends and the player receives -1 and player 2 receives 1. - If player 1 chooses to play, then player 2 observes this decision (but not the card) and chooses to Continue (C) or Quit (Q). If player 2 chooses Q, player 1 earns a payoff of 1 and player 2 a payoff of -1 regardless of player 1's card - If player 2 chooses continue, player 1 reveals her card. If the card is red, player 1 receives a payoff of 3 and player 2 a payoff of -3. If the card is black, player 1 receives a payoff of 2 and player 2 a payoff of -1 a. Draw the extensive form game b. Draw the Bayesian form game
In Las Vegas, roulette is played on a wheel with 38 slots, of which 18 are black, 18 are red, and 2 are green (zero and double-zero). Your friend impulsively takes all $361 out of his pocket and bets it on black, which pays 1 for 1. This means that if the ball lands on one of the 18 black slots, he ends up with $722, and if it doesn't, he ends up with nothing. Once the croupier releases the ball, your friend panics; it turns out that the $361 he bet was literally all the money he has. While he is risk-averse - his utility function is u(x) =, where x is his roulette payoff - you are effectively risk neutral over such small stakes. a. When the ball is still spinning, what is the expected profit for the casino? b. When the ball is still spinning, what is the expected value of your friend's wealth? c. When the ball is still spinning, what is your friend's certainty equivalent (i.e., how much money would he accept with certainty to walk away from his bet). Say you propose the following…
4.2. Game theory (Prisoner's dilemma). Often, many sectors in an economy have two main rivals, battling it out in the marketplace. There can be rivalry such as between Apple and Samsung in Phones and Laptops. Suppose Apple plans to cut its price. Samsung will likely follow suit to retain its market share. This may end up with low profits for both companies. A price drop by either company may thus be construed as defecting since it breaks an implicit agreement to keep prices high and maximize profits. Thus, if Apple drops its price but Samsung continues to keep prices high, Apple is defecting, while Samsung is cooperating (by sticking to the spirit of the implicit agreement). In this scenario, Apple may win market share and earn incremental profits by selling more. Assume that the incremental profits that accrue to Apple and Samsung are as follows: If both keep prices high (Cooperate), profits for each company increase by AED200 million (because of normal growth in demand). If one drops…
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.
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). Determine the range of values for x such that Player 2 has a strictly dominant strategy. Player 2 Left Middle Right Top (2.-1) (-2.3) (3.2) Middle (3.0) (3.3) (-1.2) Bottom (1.2) (-2.x) (2.3)
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.
In the sequential production game shown below, the actions of four players are required in order for a company's project to be successful (for example, each player could be a different division or department with the company). Player 1 Player 2 Player 3 Player 4 Act Act Act Act 10 10 10 Quit Quit Quit Quit 10 -X -X -X -X -X -X Suppose x = 5,000 (payoffs are -5,000). Suppose player 1 believes that Player 4 will quit with probability p. How does this change the game? %3D O a) If 0 0.002, Player 1 will quit. O c) If p > 0, Player 1 will quit d) The value of p is irrelevant to Player 1 O o o o
Return to the game between Monica and Nancy in Exercise U10 in Chapter 5. Assume that Monica and Nancy choose their effort levels sequentially instead of simultaneously. Monica commits to her choice of effort level first. On observing this decision, Nancy commits to her own effort level. What is the subgame - perfect equilibrium of the game where the joint profits are 5m + 4n+ mn, the costs of their efforts to Monica and Nancy are m2 and n2, respectively, and Monica commits to an effort level first? Compare the payoffs to Monica and Nancy with those found in Exercise U10 in Chapter 5. Does this game have a first-mover or second - mover advantage? Using the same joint profit function as in part (a), find the subgame - perfect equilibrium for the game where Nancy must commit first to an effort level. U10. Return to the game between Monica and Nancy in Exercise U10 in Chapter 5. Assume that Monica and Nancy choose their effort levels sequentially instead of simultaneously. Monica commits…
a) Find the Nash equilibria in the game (in pure and mixed strategies) and the associated payoffs for the players. b) Now assume that the game is extended in the following way: in the beginning Player 1 can decide whether to opt out (this choice is denoted by O) or whether to play the simultaneous-move game in a) (this choice is denoted by G). If Player 1 opts out (plays O) then both Player 1 and Player 2 get a payoff of 4 each and the game ends. If Player 1 decides to play G, then the simultaneous-move game is played. Find the pure-strategy Nash equilibria in this extended version of the game. (Hint: note that Player 1 now has 4 strategies and write the game up in a 4x2 matrix.) c) Write the game in (b) up in extensive form (a game tree). Identify the subgames of this game.

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