Question: Which of the following bestdescribes a Nash equilibrium in gametheory? A) A situation where oneplayer dominates the other player B)A situation where players cooperateto achieve the best possible outcomeC) A situation where no player has anincentive to unilaterally change theirstrategy D) A situation where playerscollude to maximize their joint payoffs

Strategy: It is an action plan or decision-making process that players adopt to achieve their…

Answered: Question: Which of the following best…

Question: Which of the following best describes a Nash equilibrium in game theory? A) A situation where one player dominates the other player B) A situation where players cooperate

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION 12 This is a HOT SPOT question. You will need to evaluate the picture of the game below, and answer the question by clicking on a specific area (the hot spot) of the picture. Question: Are there any dominant strategies in this game? If there are, click on the box that corresponds to that dominant strategy (either UP, DOWN, LEFT, or RIGHT). If there aren't any anywhere outside of these boxes. If there are dominant strategies for both players, clicking on only one of them will suffice. Player 1 Player 2 Selected Coordinates Clear UP DOWN LEFT 45, 80 70, 100 RIGHT 50, 150 60, 60
QUESTION 2 In the game above, what is/are the sub-game perfect Nash equilibrium? (up, up) (up, down) ( down, up) (down, down) No equilibrium exists QUESTION 2 Up Down Player 1 No equilibrium exists Up In the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) □ (down, down) Down Up Down Player 2 P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95
QUESTION 3 Up Down In the game above, what is/are the sub-game perfect Nash equilibrium? Ⓒ (up,up) (up,down) Player 1 (down, up) (down, down) No equilibrium exists Up Down Up Down Player 2 P1 gets $25 P2 gets $25 P1 gets $7 P2 gets $30 P1 gets $13 P2 gets $9 P1 gets $8 P2 gets $6
Player 2 Left Right P1: $4 Player 1 Up P2: $1 P1: $10 Down P2:s10 Which of the Nash Equilibrium to this game are efficient? [Check all that apply] A) (up, left) B) (down, left) C None are efficient (D) (up right) E (down, right) Last saved 4:31:15 PM P1:S1 P2: $6 P1: $0 P2: $11 Grading
Up Down Up Up Down Down Player 1 Player 2 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No EFFICIENT equilibrium exists P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95
(The Beckhams' dilemma) Victoria and David are husband and wife. They both prefer ciean to dirty house but neither likes to clean the house. Their payoffs are given in the table below. Victoria Clean Don't clean 0,8 Clean 5,5 David Don't clean 8,0 1,1 a) Let say they play the clean house game only once, what is the Nash equilibrium? b) Let say Victoria and David has to decide whether to clean or not every day for indefinite number of days. How grim-trigger strategy will be our subgame perfect Nash equilibrium? In other words, what is the patience rate that ensure Victoria and David maintain the cleanliness of the house?
QUESTION 4 Suppose there are 2 players in a non- cooperative game theory situation. Player A can move Up or Down while Player B can choose Left or Right. The following matrix contains the payoffs that each player receives under 4 scenarios. The first number in each cell refers to the payoffs for Player A. Player A Up Down A. B. C. 10, 60 D. 20, 80 Player B Suppose Player A moves first and Player B moves second. There is one equilibrium, Up, Left Left There is one equilibrium: Down, Right. 50, 90 40, 50 There are two equilibria, (Down, Left) and (Up, Right) Right There is one equilibrium in this game, Up Right
Player 1 Up Down [Select] Left 2,4 6,5 Player 2 In the above game, player 1 would play [Select] Right 1,0 4,2 , player 2 would play resulting in a Nash Equilibrium of [Select]
5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
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