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: ........

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

In the following normal-form game, what strategies survive iterated elimination of strictly dominated strategies?   L C R T 2,0 1,1 4,2 M 3,4 1,2 2,3 B 1,3 0,2 3,0

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

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