(2) Consider the following two-player norma. M 5,1 6,3 1,4 0,0 2;1 1, 1 R Player 1/Player 2 2,2 3,3 3,60 -2,0 2,-1 1,4 2,5 Cu Co 1,2 1 32 i. Which strategy profiles survive iterated elimination of strictly dominated strategies (including pure-strategy and mixed- strategy dominances)? ii. Find all pure-strategy Nash equilibria. iii. Final all mixed-strategy Nash equilibria (excluding the ones

(2) Consider the following two-player norma. M 5,1 6,3 1,4 0,0 2;1 1, 1 R Player 1/Player 2 2,2 3,3 3,60 -2,0 2,-1 1,4 2,5 Cu Co 1,2 1 32 i. Which strategy profiles survive iterated elimination of strictly dominated strategies (including pure-strategy and mixed- strategy dominances)? ii. Find all pure-strategy Nash equilibria. iii. Final all mixed-strategy Nash equilibria (excluding the ones

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Consider the following game in strategic or normal form. A2 B2 C2 A1 1,0 | 1,2 -2,1 B1 6,2 0,3 2,3 c1 2,2 -2,1| 2,3 a. Use the iterative elimination of strictly dominated strategies to reduce the game as much as possible. b. What is the set of rationalizable strategies for each player? c. What is/are Nash equilibrium(s) in this game? d. Explain the differences between cooperative and non- cooperative games. What are the fundamental hypotheses about the behavior of the persons in Game theory?
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INFINITE REPETITION Consider the infinitely repeated game constructed from the following stage game. bị b2 a1 8,8 3,13 a2 13,3 0,0 Suppose that both players use the discount factor d to evaluate future payoff streams. What is the smallest value of d such that there exists a subgame perfect Nash equilibrium in which the action profile is played in all periods? (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)
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Explain all will rate what is always true for a pure nash equilibrium of a two-person non zero-sum game A.No player can improve his payoff with a unilateral change of strategy B. it is a Pareto maximum of the payoff matrix C. No player can worsen the payoff of his opponent with a unilateral change of strategy D. It gives worse payoffs to both players than any berge equilibrium
4. Consider a normal form game with N= {1,2} and S= {A,B,C,D} x {W,X,Y,Z}. Assume that L1 allows to eliminate D and X, L2 allows to eliminate B and C, and L3 allows to eliminate Z. Provide payoffs that lead to this outcome. State the rationality assumptions explicitly.
Consider the following game. Player 1 has three actions: A, B, C. Player 2 has three actions: a, b.c. Payoffs are as follows: a b A 5,3 8,5 1,2 2,6 6,7 4,5 C 4,4 0,2 9,3 Which of the following aciton profile survives the iterated elimination of strongly dominated actions? A. (A,a) O B. (B, c) O C. (A, b)
Pay-offs (in terms of profit) for the two firms are give Firm2 startegies Firm1 Strategies C B W C [4, 4] [0, 5] [-1, 5] [5, 0] [2, 2] [-1, 1] W [5, -1] [1, -1] [0, 0] a)What is a dominant strategy for each player? b)What are the possible pure strategy Nash equilibrium/equilibria to the one-shot play of this game? c) Explain the likely out the game
Consider a game with both simultaneous-move and sequential move in the attached file, which is same one with the former question. Choose all payoffs that the players get at subgame perfect Nash equilibria. А. (3,3) В. (4,2) С. (2,4) D. (5,5) Е. (6,4) F. (4,6) 2 2 1 A В А 3,3 4,2 B 2,4 2 C D 1 C 5,5 6,4 4,6 5,5 1.
6.
Which of the following is true of the normal form game below: P1. 2 X Y U Pl. 1 M D a. D is a dominated strategy for Player 1 b. U is a dominant strategy for Player 1 C. Z is a dominant strategy for Player 2 d. All of the above e. None of the above Y Z 0,4 4,5 1,5 5,3 2,0 8,3 4,2 3.7 0,1 3