Consider the following game in normal form. Player 2 L N Player A 8,11 0,0 1 B9,-1 0.5,5 Assume that the game will be repeated infinitely many times, and that player 2 is playing a grim trigger strategy. That is, he starts in the first period with L and plays L as long as player 1 does not deviate from A: If player 1 deviates from A, i.e., if player 1 plays B, player 2 chooses N in the next period and all future periods. How large needs to be, such that player 1 has no incentive to depart from A in the first period? 062/1/1/00 082 / 0. 062 1/1/000 062/1 None of the answers is correct.

Consider the following game in normal form. Player 2 L N Player A 8,11 0,0 1 B9,-1 0.5,5 Assume that the game will be repeated infinitely many times, and that player 2 is playing a grim trigger strategy. That is, he starts in the first period with L and plays L as long as player 1 does not deviate from A: If player 1 deviates from A, i.e., if player 1 plays B, player 2 chooses N in the next period and all future periods. How large needs to be, such that player 1 has no incentive to depart from A in the first period? 062/1/1/00 082 / 0. 062 1/1/000 062/1 None of the answers is correct.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
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Consider the infinite repeated two-player game where at each stage the play- ers play the non-zero-sum game given by A В A (5, 5) (0,7) В (7, 0) | (2, 2) (a) Consider the following strategies: SA: always play A. SB: always play B. • St: play A on the first stage, thereafter copy what the other player did in the preceding stage. Suppose that the total payoff involves a discount factor 8, and that both players are restricted to the pure strategies SA, SB, and sT. Determine the set of d for which (ST, ST) is a Nash equilibrium. (b) Use the one stage deviation principle to determine whether the pair (ST, ST) is a subgame perfect Nash equilibrium for some range of val- ues of 8.
Consider the following simultaneous game. a. b. C. d. Player 1 U Player 2 L 8,8 3,0 R 3,3 8,3 What are the pure-strategy Nash equilibria? Identify. Find whether there are any mixed-strategy equilibria. Assume now the game above is being modified as a sequential game where player 1 would move first and player 2 second. Find all Nash and subgame perfect equilibria for the game. Would a Nash equilibrium always be Pareto efficient? Use your answer in (a) to explain.
Player 2 A B C А 2, 2 6,1 1,1 Player 1 B 1,6 5,5 1,1 1,1 1,1 4,4 Consider the simultaneous move game represented in normal form by this payoff matrix. Suppose that the game is repeated for two periods. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. (B, B) is played in the first period, (C, C) is played in the second period. (A, A) is played in both periods. (C, C) is played in both periods.
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A 201.
11. The following payoff table involves two players each of whom has three possible moves. L M N L 30,15 45,35 55,25 M 25,35 20,20 30,50 N 15,35 35,40 15,15 a. Are there any dominant strategies in this game?