1.Consider the two-player game described in figure 1. Player 1 has three possibleactions to choose from and player 2 has two. The payoffs to each player are shown inthe normal-form representation of the game below.(a)Player 2LRU 5,1 4,0Player 1 M 6,0 3,1D 7,3 5,4Figure 1Do either players have any dominated strategies?(b)What is the Nash Equilibrium of this game?

PLAYER 2LR PLAYER 1U5, 14, 0M6, 03, 1D7, 35, 4 a) A dominated strategy is one that always yields a…

Answered: 1. Consider the two-player game…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Find the dominant and dominated strategies in the following games (in case players have such strategies) Is there any dominant strategy equilibrium in any of these games? (b) Player 2 V W X Y A 2,5 4,4 5,5 | 0,4 | 1,5 B 5,3 3,3 4,3 | 2,2 | 1,0 Player 1 C 6,0 | 3,0 | 1,1 | 1,1 0,1 D 6,2 3,0 4,2 3,2 | 1,2 E 1,1 5,1 | 4,2 | 1,0 | 0,2
11) In the following game, list any dominant or dominated strategies. Then, solve the game Player 2 Left Center Right Player 1 Up 1,2 4,6 5,5 Down 6,3 2,4 3,1
3
Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?
Player 1 Player 2 2 X 4 2 y 1 3 X 2 2 b y O 6 3 1 4 2 X 1 5 y O Consider the game tree given above: a. Write out the set of pure strategies for all players. b. Find the Subgame Nash equilibria of this game.
9. For the payoff matrix below, consider a sequential version of the game in which Player 2 moves first and then Player 1 moves second. Which of the following is not a correct statement? Player 1 Top Center Bottom Left 1,2 5,1 6,0 Player 2 Middle 7,1 11,2 -4,3 Right 10,4 1,0 8,5 The subgame perfect payoffs coincide with those of a Nash equilibrium b. Depending on Player 2's move, Player 1 will sometimes optimally choose Bottom c. Player 2 will choose Right in the subgame perfect equilibrium d. Player 2 would be willing to pay a positive $ amount to move first rather than second e. Player 1 would be willing to pay a larger $ amount than Player 2 to move first
3. Which is the Subgame Perfect Equilibrium of this game? [Here ((Not Play, Steal), (Trust)) indicates that player 1 chooses Not Play at the first decision node and Steal at the second decision node, and 2 chooses Trust at his unique decision node.] 1 Not Play Play 1 2 1 Trust Distrust 1 0 Steal Share 2 10 5 0 5 O a) ((Not play, Steal),(Distrust)) b) ((Not play, Share), (Distrust)) O c) ((Not play, Steal), (Trust)) O d) ((Play, Steal), (Distrust)) Oe) ((Play, Share), (Trust))
4. Consider a two player game with Fred and Barney, who tal turns removing matchsticks from a pile. They start with 33 matchsticks, and Fred goes first. On each turn, ecach player may remove either one, two, three, four, or five matchsticks. The player to remove the last matchstick wins the game. What are the optimal strategies for each player? Who will win? b. Suppose now that they can remove up to six matchsticks, how will the optimal strategies change for- each player? a.
1. Consider the following game. 21 Player 1 U D Player 2 LR 2,4 4,2 6,2 2,4 ium. thi c) Are there any pure strategy Nash equilibria in this sequential game?
60B- What is the Nash equilibrium for this game and identify the profit each player gets at this solution 5 m
1. Consider the following game matrix. Player A Answer: Top Bottom Left a, b e, f Player B Right c, d g, h (a) If top and left are strictly dominant strategies, then what do we know the relationship of the parameters? (b) If (top, left) is a Nash equilibrium, then what do we know the relationship of the parameters? Answer: (c) If top and left are strictly dominant strategies, will (top, left) be a Nash equilibrium? Why? Answer: (d) If (top, left) is a Nash equilibrium, must the strategies be strictly dominant strategies? Why? Answer:
A 201.

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