Homework Answers
When player one selects hawk, player two selects Dove. When player one selects Dove, player two selects hawk.
Similarly when player two selects hawk, player one selects Dove and when player two selects Dove, player one selects hawk.
This indicates that there are two Nash equilibria in this case: Dove hawk and hawk Dove.
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7. Consider the simultaneous hawk-dove game belon. What are the Nash Equilibria of the game? (5pts)...
Consider the following game: a) Identify all Nash Equilibria (Pure Strategy and Mixed) of this simultaneous...
Consider the following game:
a) Identify all Nash
Equilibria (Pure Strategy and Mixed) of this simultaneous game.
b) Identify a trigger strategy for
each player that sustains (B,B) as an equilibrium in an infinitely
repeated game. For what interest(discount) rates will this outcome
be sustainable?
Firm 2 А B A -5,-5 195,-50 Firm 1 -50,215 45,75
6. Consider the following game: a. Identify all Nash Equilibria (Pure Strategy and Mixed) of this...
6. Consider the following game: a. Identify all Nash Equilibria (Pure Strategy and Mixed) of this simultaneous game. b. Draw the two extensive form games that arise from each firm moving first. What are the Subgame Perfect Equilibria of these games? c. Identify a trigger strategy for each player that sustains (B,B) as an equilibrium. For what interest (discount) rates will this outcome be sustainable?
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10...
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10 20.30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.
Some Game Theory Problems 3. Find all of the pure strategy Nash Equilibria of the following simultaneous move game....
Some Game Theory Problems 3. Find all of the pure strategy Nash Equilibria of the following simultaneous move game. After solving it as a simultaneous move game, write it as a sequential move game with column moving first. Drow the game tree and solve for the Subgame Perfect Nash Equilibrium. Column 9,4 1,10 15,7 15,5 14,8 3,10 12,18 20,12 Row C 7,8 6,8 20,10 3,3 15,9 15,0 14,2 9,1 20,18 2,9 10,14 19,20
Q. 1. Consider the following pay off matrix of the two players: A and B. What are the Nash equilibria in the game? [3 M...
Q. 1. Consider the following pay off matrix of the two players: A and B. What are the Nash equilibria in the game? [3 Marks] Player 2 Player 1 Strategy A Strategy B Strategy C Strategy D 4.2 11,2 12. 14 Strategy E 13.6 0,0 4. 11 Strategy F 1.3 15, 10 5.4
What is (are) the Nash equilibrium (equilibria) in the game shown below? Player 2 Cooperate Defect...
What is (are) the Nash equilibrium (equilibria) in the game shown below? Player 2 Cooperate Defect Cooperate 5,5 0,10 Player 1 Defect 10,0 1.1
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There may be none, or multiple). Note: assume the payoffs in the boxes are "positive"- i.e. higher numbers represent better payoffs. Player 2 Strategy Strategy #2 ii Player 2 Strategy Strategy #1 #1 # 2 R 50 20 Strategy 15 20 100 Strategy 70 20 #1 #1 10 10 20 5 Strategy Strategy 70 Player 2 Strategy Strategy #1 60 100 #2 15 Player 2...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There may be none, or multiple). Note: assume the payoffs in the boxes are "positive" -- i.e. higher numbers represent better payoffs. Player 1 Player 2 Strategy Strategy #1 #2 Strategy A 20 B 100 #1 20 No a Strategy No 5 100 Player 2 Strategy Strategy Player 1 Strategy #1 Strategy Player 2 Strategy Strategy #1 #2 15 R 50 70 20 x 20...
9. Find the Nash equilibrium or equilibria for the following three-player, simultaneous, non- cooperative, non-repeated game?...
9. Find the Nash equilibrium or equilibria for the following three-player, simultaneous, non- cooperative, non-repeated game? Maeve: Fish Dolores Left 1, 2,31, 3, 2 CenterRight 1,3, 1 Middle 2, 0,32,4, 23,4,3 4, 2,2 Up Teddy Down 2,1,11,2,1 Maeve: Sea Shell Dolores Left CenterRight 1,12,0,0 3, 3,4 3, 1,23, 2,4 2,1, 3 0,0,41,1 Teddy Middle 2,1,2 2,4,3 Down Maeve: Turtle Dolores Center Rig Left 2,1,23,2,1 Up Middle 4, 3, 22,2,14,2,2 Down 2, 3, 0 Teddy 0, 0, 01,2,0 1,3, 1
Froblem #5: Convert extensive-form to strategic-form, find Nash equilibria and subgame. perfect Nash equilibria (12...
Froblem #5: Convert extensive-form to strategic-form, find Nash equilibria and subgame. perfect Nash equilibria (12pts) Consider the following extensive-form game: Veto Y Don't Veto In this game, Players 1 and 2 are deciding on a course of action, which may be X, Y, or Z Player 2 is the one who actually makes the choice, but first Player may choose to veto Y, which is the option Player 1 prefers the least. a) List all the strategies available to Player...
Consider the following game:
a) Identify all Nash
Equilibria (Pure Strategy and Mixed) of this simultaneous game.
b) Identify a trigger strategy for
each player that sustains (B,B) as an equilibrium in an infinitely
repeated game. For what interest(discount) rates will this outcome
be sustainable?
Firm 2 А B A -5,-5 195,-50 Firm 1 -50,215 45,75
Consider the following simultaneous game: Player 2 L R Player 1 U 30,20 -10-10 D -10-10 20.30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.
Some Game Theory Problems 3. Find all of the pure strategy Nash Equilibria of the following simultaneous move game. After solving it as a simultaneous move game, write it as a sequential move game with column moving first. Drow the game tree and solve for the Subgame Perfect Nash Equilibrium. Column 9,4 1,10 15,7 15,5 14,8 3,10 12,18 20,12 Row C 7,8 6,8 20,10 3,3 15,9 15,0 14,2 9,1 20,18 2,9 10,14 19,20
Q. 1. Consider the following pay off matrix of the two players: A and B. What are the Nash equilibria in the game? [3 Marks] Player 2 Player 1 Strategy A Strategy B Strategy C Strategy D 4.2 11,2 12. 14 Strategy E 13.6 0,0 4. 11 Strategy F 1.3 15, 10 5.4
What is (are) the Nash equilibrium (equilibria) in the game shown below? Player 2 Cooperate Defect Cooperate 5,5 0,10 Player 1 Defect 10,0 1.1
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There may be none, or multiple). Note: assume the payoffs in the boxes are "positive"- i.e. higher numbers represent better payoffs. Player 2 Strategy Strategy #2 ii Player 2 Strategy Strategy #1 #1 # 2 R 50 20 Strategy 15 20 100 Strategy 70 20 #1 #1 10 10 20 5 Strategy Strategy 70 Player 2 Strategy Strategy #1 60 100 #2 15 Player 2...
Questions 7-10 For each of the following games, please identify the Nash equilibrium or equilibria. (There may be none, or multiple). Note: assume the payoffs in the boxes are "positive" -- i.e. higher numbers represent better payoffs. Player 1 Player 2 Strategy Strategy #1 #2 Strategy A 20 B 100 #1 20 No a Strategy No 5 100 Player 2 Strategy Strategy Player 1 Strategy #1 Strategy Player 2 Strategy Strategy #1 #2 15 R 50 70 20 x 20...
9. Find the Nash equilibrium or equilibria for the following three-player, simultaneous, non- cooperative, non-repeated game? Maeve: Fish Dolores Left 1, 2,31, 3, 2 CenterRight 1,3, 1 Middle 2, 0,32,4, 23,4,3 4, 2,2 Up Teddy Down 2,1,11,2,1 Maeve: Sea Shell Dolores Left CenterRight 1,12,0,0 3, 3,4 3, 1,23, 2,4 2,1, 3 0,0,41,1 Teddy Middle 2,1,2 2,4,3 Down Maeve: Turtle Dolores Center Rig Left 2,1,23,2,1 Up Middle 4, 3, 22,2,14,2,2 Down 2, 3, 0 Teddy 0, 0, 01,2,0 1,3, 1
Froblem #5: Convert extensive-form to strategic-form, find Nash equilibria and subgame. perfect Nash equilibria (12pts) Consider the following extensive-form game: Veto Y Don't Veto In this game, Players 1 and 2 are deciding on a course of action, which may be X, Y, or Z Player 2 is the one who actually makes the choice, but first Player may choose to veto Y, which is the option Player 1 prefers the least. a) List all the strategies available to Player...
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