Consider the following game: Mary D E F John A 6, 2 8, 4 3, 3 B 2, 6 8, 5 9, 5 C 5, 7 1, 3 -1, 6 What is the outcome by elimination of dominated strategies? a. (B, F) b. (B, D) c. (A, F) d. (A, E) e. (A, D) f. (B, E) g. (8, 5)
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Consider the following game:
|
|
Mary |
|||
|
D |
E |
F | ||
|
John |
A |
6, 2 |
8, 4 |
3, 3 |
|
B |
2, 6 |
8, 5 |
9, 5 |
|
| C |
5, 7 |
1, 3 |
-1, 6 |
What is the outcome by elimination of dominated strategies?
Step by step
Solved in 2 steps
- 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? (a) Player 2 L R Player 1 U 5,5 3,6 D 6,3 4,4 (b) Player 2 W X Y Z 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 VWhat is the Nash Equilibrium of this game? Firm Develop Don't Develop Don't Develop, Protect O Develop, Don't Protect Protect Don't Develop, Don't Protect O Develop, Protect -3,2 1,1 Government Don't Protect 8,10 0,2Refer 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
- one two X, 14 three four Firm B Low Firm A Sell High 6, Y Buy Low Let X = 9, Y = 15 and Z=10. This game has 10, Z Firm B High 8,8 Nash equilibrium.1. You (row)/Your Crush (column) McElroy Corcoran The Dining Hall Game McElroy 3,2 0,0 a) Represent this game in extensive form b) How many subgames does this game have? Corcoran 1,1 2,3Problem 1 Consider the following two-person game: 1 2 C ea Prsover's D U 4, 7 6,0 10, 4 11, 5 M 5, 4 7,5 0, 3 6, 3 D 3, 12 5, 10 12, 5 8, 16 Use successive elimination of dominated strategies to find the optimal strategies.
- A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?Question 1 A B C 0 Which of the following strategies are weakly dominated in this game? D F B OE F 4,3 4,3 4, 4, 1 5,2 5,3 5, 1 4,2 4,3 3, 1 OC DE OAWhich is the correct mixed strategy Nash equilibrium for the below game? A B Confess Confess (3,2) Doesn't (0,0) confess a. (2/5); (3/5) b. (1/4); (3/4) c. (1/2); (1/2) d. (1/3); (2/3) Doesn't confess (0,0) (2,3)
- Consider the game in the table below. What is firm A's payoff from their best response to Firm B choosing Down? Firm A Left Straight Right Up 7,5 3,7 1,3 Firm B Middle 8,14 2,7 4,17 Down 9,13 1,3 2,16 164. Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff and the second entry is Animal B's payoff: Animal A Hawk (rows)/Animal B (columns) Hawk Dove (-10,-10) (0,20) Dove (20,0) (8,8) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. (a) Explain why there cannot be an equilibrium where all animals act as Doves. (b) Explore whether there are any Nash equilibria in pure strategies and explain which these are and why they are equilibria.Refer to the accompanying figure. In this game, how many dominant strategies does Player B have? Player B Player A Up Down Multiple Choice 0 4 2 Left 5 for A 30 for B -2 for A 10 for B Right 10 for A 12 for B 8 for A 15 for B