Question 2 (Choices Involving Strategy): Suppose there are two competing Gyms in a local town. Each gym is individually owned and has three pricing levels to choosefrom: Low, Medium and High (PL,PM, and PH). Consider the table below as the outcomes for each combination of strategies (they are yearly profits in the thousands). Can youpredict the outcome using ONLY iteratively dominated strategies? Why or why not? Find the Nash Equilibrium(a) using best responses. Is this the best outcome?Now, suppose that there was a sudden increase in the cost of equipment that meant the low price was no longer viable, and both choosing the medium price level meant only 50(thousand) profit for each gym. Nothing else changes. What is the pure and mixed strategy Nash equilibrium of this new game? Gym 1 is on the left and Gym 2 is on the top.The first number inside every box is Gym 1's profit and the second (after the comma) is Gym 2's profit. (10 Marks)PL PMPHPL125, 125200, 75375,50PM75, 250225, 225400, 100PH50,375100, 400325, 325

To answer this question, let's analyze the game theory problem step by step:1. Nash Equilibrium in…

Answered: Question 2 (Choices Involving…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two car producers, Firm A operates in Country A and Firm B operates in Country B, are considering producing a new 8-seater Multi-Purpose Vehicle (MPV)for the international market. The payoff matrix is as follows (payoff values are in millions of dollars). The above payoffs imply that the international market demand is large enough to support only one producer. If both firms produce, both will sustain a loss. (i) Explain and solve for the Nash equilibrium in this game. (ii) Suppose the government of Country A decides to subsidise Firm A with $25 million if it produces. Revise the payoff matrix to account for this subsidy. What is the new equilibrium outcome? Compare the two outcomes and discuss the effect of the subsidy.
Consider a coordination game where each of two agents picks a number between 1 and 1000. The players get a prize of $1000 each if their numbers are the same, and $0 otherwise. In this game, there exists(A) a thousand of pure-strategy Nash equilibria;(B) an iterated dominant-strategy equilibrium;(C) a dominant strategy equilibrium;(D) none of the above.
Which of the following best defines a Nash Equilibrium? A) A situation where each player maximizes their own payoff without regard to the strategies of others. B) A situation where no player can improve their payoff by unilaterally changing their strategy. C) A situation where players cooperate to achieve the highest collective payoff. D) A situation where each players strategy maximizes the opponents payoff.
Problem #4: Bayesian Nash Equilibrium Consider the following game, which has two states of nature shown in the two game tables below: "Harmful" (p = 1/3) "Helpful" (1-p = 2/3) Player 2 X Y 3, 2 Player 2 Y 2, 3 3, 2 1,0 0,1 A 0,1 3,2 A Player 1 Player 1 В 0,1 B a) Assume that Player 1 knows what the true state of nature is when playing this game, but Player 2 does not. Find all of the game's Bayesian Nash equilibria. (Hint: It may help to arrange the game tables appropriately.) b) Now, assume that Player 2 knows the true state of nature, but Player 1 does not. Find all of the game's Bayesian Nash equilibria.
The payoff matrix depicts potential payoffs in a non-sequential, non-repeating game. Blue numbers are for Player 1 and red numbers are for player 2. (This exact payoff matrix appears in 3 other questions on this exam.). The cooperative (collusive) equilibrium is: Player 1 (70,80) 0000 (30,20) (40,40) (10,90) Strategy C Strategy D Player 2 Strategy A 40, 40 10,90 Strategy B 30, 20 70, 80
Consider a beauty-contest game in which n players simultaneously pick a number between zero and 100 inclusive; the person whose number is closer to half of the average number wins a prize. What is the unique Nash equilibrium of this game? What number will a level-3 thinker pick?
Assume there are two firms X and Y, considering which of two alternative prices to charge, £25 or £19 for X and £20 or £15 for Y. The firms make their decisions simultaneously: i.e. neither firm knows the price choice of its rival. The various profits are illustrated in the following pay-off matrix: Strategies and payoffs for X are in blue and for Y in red. (a) What is firm Y’s best response to each of the two different prices firm X could charge? Does firm Y have a dominant strategy? (b)What is firm X’s best response to each of the different prices firm Y could charge? Does firm X have a dominant strategy? (C) What is/are the Nash equilibrium/equilbria? What is the most likely outcome of this game? Explain your answer.
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?
Consider the following game matrix with two players- Player 1 and Player 2 with their respective strategies. Which of the following statements is correct such as x>y>b>a Players Player2 Player 1 A B C D (Y, Y) (b, x) (x, a) (AE) is the one of many Nash equilibria (C) is the unique Nash equilibria (C. D) is the unique Nash equilibria (A. E) and (B. F) are two Nash equilibria E (a, b) (x, y) (y, a) F (a,x) (a, b) (b, b)
Player 2 1 2 3 1 (0,2) (1,0) (0,2) (0,2) Player 1 2 (1,0) (1,0) 3 (0,2) (1,0) (0,2) 1. Find all pure. strategy Nash equilibria 2. Does the game have a mixed strategy equilibrium? If so, find one. Otherwise, provide an explanation

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