Question: Determine the set of rationalizable strategies for each of thefollowing games.Player 2Player 2(0, 4)(3, 3)(4, 0)Player 2(2,0)(3, 4)(1,3)(4, 2)(2, 3)(4,0)(3, 3)(0, 4)(1,1)Player 1Player 1(1,2)(0,2) | (3,0)Player 2DD(5, 1) | (0, 2) | Player 1(4, 6)(3, 5)(6, 3)(0, 1)(2,1)Player 2(8, 6)(1,0)(0,8)(8, 2)(0, 1)(2, 6)(5, 1)(4, 4)(1,0)Player 1(6,0)(2,8)DDPlayer 2(8, 10)(6, 4)(2, 2)(0,0)(0,0)(3,3)(4, 1)(8, 5)Player 1Player 1BBPlayer 2Player 2(8, 10)(6, 4)(3, 10)(6, 4)(4, 1)(8, 5)(4, 1)(8, 5)Player 1APlayer 1BB

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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 business partners jointly own a firm and share equally the revenues. They individually and simultaneously decide how much effort to put into the firm. Let s₁ and s2 denote the effort choices of partner 1 and partner 2, respectively. Assume si € [0, 4]. The cost of effort is given by s? for i E {1, 2}. The firm's revenue is given by 4(81 +82 + bs182) where 0 ≤ b ≤ 1. (Note that the parameter 6 reflects the synergies between the effort levels. b> 0 implies that the more one partner works, the more productive the other partner is.) The payoffs for partners 1 and 2 are: u₁ (81, 82) u2 (81, 82) - = 1 [4(81 +82 +68182)] − 8² - 1 [4(81 +82 + bs182)] – $²
(c) Consider the following two-player, zero-sum game: Y1 Y2 X1 -2 8 X2 10 -5 What is the outcome of this game?
Question 1 Using your knowledge of the "method of elimination.of dominated strategy". solve for the equilibrium solution(s) to the following pay-off matrix for two players. Player A Player B Strategyl Strategy 2 Strategy 3 Strategy 4 Strategy 5 Strategy1 (40, 200) Strategy 2 (60, 25) Strategy 3 (88, 55) (55,102) (45, 142) (109) 42) K09. 120) (50, 100) (99, 155)70 la. (80. 100) K104, 55) (44,90) (100,50) C403)165)(17 190 (60, 160) (155,115) (95.120) (50, 90) (84, 100) Strategy 4 Strätegy 5 172) 140) (85, 145) (48, 200) 123)125) (100, 145) Is your solution in "a above unique? Why? b. Present the following extended form of pay-off matrix in a normal form pay-off matrix for the player Extended Form of Pay-»ff Matrix Player B Strategy 1 (40, 20) (30,25) Strategy 2 (90, 300) (85.55) 30 25 Player A Strategy 1 Strategy 2 20
Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1
Player 1 R Player 3 Player 2 а Player 3 Player 3 (3) (:) () () G) (F) 1 4 2 7 (a) Solve the game by backward induction and verify that the strategies found by backward induction constitute a Nash equilibrium. (b) Identify all other pure strategy Nash equilibria of the game. (c) Argue that all Nash equilibria found in (b) do not satisfy the principle of sequential rationality.
(a) Consider the following bimatrix of a normal form game. Show that the set of strategies that survive elimination of weakly dominated strategies depends on the order in which the weakly dominated strategies are eliminated. Player 2 L R 1,1 0,0 M| 1,1 0,0 | 2,1 Player 1 2,1 (b) Find an example of a game where the unique Nash equilibrium in pure strategies would not survive the eliminination of weakly dominated strategies. (c) Find an example of a game where both players' strategies are weakly dominated in the Nash equilibrium.
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(d) Consider a simultaneous-move game between two firms choosing to sell their product at either £6, £7 or £8. The actions and payoffs are given in the matrix below. Firm 2's Prices £6 £7 £8 Firm 1's prices £6 4, 5 3, 5 2, 1 £7 0,4 2, 1 3,0 £8 -1, 1 4, 3 0, 2 What are the Nash equilibria of this game? Game theory is often used by firms competing under an oligopoly as a means of determining their best strategy. Why is game theory a useful tool and which characteristics of an oligopoly make it particularly useful for firms competing in this market structure? One outcome of an oligopoly is that firms may have an incentive to collude. Explain some of the conditions that make collusion more likely to occur and how game theory can explain why collusive agreements often break down.
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A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?
Can you help me with the question below? What is [are] the Nash Equilibrium [Equilibria] of this game? A) (10;10) and (20;20) B) (30;30) C) (10;20) and (20;10) D) (20;20) E) (30;30)

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