Question 3. Consider the following game, and calculate the following: Player 2 X Y Z A 1,3 1,7 5,2 B 2, 2 -3, 5 2,0 C5, -4 6,0 9,-1 Player 1 Q3)a) All Dominance Relations: ................ Q3)b) Strictly Dominated Strategies: .. ...... ............... Q3)c) Strictly Dominant Strategies: ...... ......... Q3)d) Rational Outcome: ........

Question 3. Consider the following game, and calculate the following: Player 2 X Y Z A 1,3 1,7 5,2 B 2, 2 -3, 5 2,0 C5, -4 6,0 9,-1 Player 1 Q3)a) All Dominance Relations: ................ Q3)b) Strictly Dominated Strategies: .. ...... ............... Q3)c) Strictly Dominant Strategies: ...... ......... Q3)d) Rational Outcome: ........

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
Refer to the accompanying game. Firm A Firm B Low Price High Price Low Price (10,9) (15,8) High Price (−10,7) (11,11) What are the secure strategies for firm A and firm B, respectively?
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QUESTION 12 This is a HOT SPOT question. You will need to evaluate the picture of the game below, and answer the question by clicking on a specific area (the hot spot) of the picture. Question: Are there any dominant strategies in this game? If there are, click on the box that corresponds to that dominant strategy (either UP, DOWN, LEFT, or RIGHT). If there aren't any anywhere outside of these boxes. If there are dominant strategies for both players, clicking on only one of them will suffice. Player 1 Player 2 Selected Coordinates Clear UP DOWN LEFT 45, 80 70, 100 RIGHT 50, 150 60, 60
Refer to the following payoff table: Firm A's Advertising Budget Multiple Choice Low O Medium High Firm A High Firm A High A Firm B Medium D G Low $900, $900 $1,000 $800 Firm B's Advertising Budget Medium B E H $820, $1,220 $950, $1,025 $875, $920 $800, $875 After the first round of elimination, are there any dominant strategies? If so, which one(s)? C Neither firm has a dominant strategy after the first round. F High $1,060, $1,100 $1,040, $1,000 $1,025, $1,175
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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a) Clearly indicate the eliminated dominated strategies. Apply the EIE algorithm, and determine the solution set of the game in normal form. b) Assuming that each player would not choose strategies that are strictly dominated, determine the Nash equilibria of the reduced game J2 (3,1) (4, 2) (2, 0) (0, 4) (1, 5) (3,0) (1, 3) (2, 2) a J1 (4, 1) (2, 5) (2,6) (5, 2)
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:
Dizz Cut price Maintain price Perlis Cut price (-1,-1) A (2,-2) B Maintain price (-2,2) (1,1) D Figure 12 Payoff matrix for two firms in oligopoly Two firms, Perlis and Dizz, produce washing powder in a market characterised by oligopoly. Each firm can increase its market share and profits by cutting its price relative to its rival. However if both firms cut prices they both suffer a fall in profit. This situation may be characterised as a game and Figure 12 shows the payoff matrix for this game. Figure 12 also labels each cell in the payoff matrix with a letter, A, B, C or D. Based on the information in the payoff matrix, decide which cells, if any, correspond to a Nash equilibrium. Select one answer. Select one: O There is no Nash equilibrium O D O A O A and D
ITERATIVE DOMINANCE Consider the following game in strategic form. b1 b2 b3 9,4 11,5 a1 1,6 6,7 3,1 a2 2,3 7,3 7,8 a3 4,2 Which of the following payoff profiles survive iterative deletion of strictly dominated strategies? (Mark all profiles that survive.) O O O O O O O O O
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