Homework Answers
A.
B.
An unconditional strategic move is a strategy or action that influences the beliefs or actions of the other players in a favorable way. It should be analyzed sequentially. Player 2 knows that T strictly dominates B for player 1 so player 1 would never choose B. Given that, player 2 would always choose L (as L strictly dominates R). There is no unconditional strategic move that makes player 2 better off. The payoff would remain (5,2).
C.
Player 2 cannot help himself using a conditional strategic move either. If he chooses L, player 1 chooses T. If he chooses R, Player 1 chooses M and he gets a lesser payoff than the pure strategy NE.
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Question 1 (15 polnts) Consider the following simultaneous-move game Player 2 ILIR T15. 2 | 2,0 B 3,30, 5 A. Find the pure-strategy Nash equilibrium of this game. Player M B. Can player 2 help hi...
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4...
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4 DOWN 2,3 3,2 a. If there is a Nash equilibrium in pure strategies, what is it and what are the payoffs? b. If there is a Nash equilibrium in mixed strategies, what is it and what are the expected payoffs? 3. Continue with the previous game but suppose this was a sequential game where Player A got to go first. a. Diagram the game...
4. Find all of the pure strategy Nash Equilibrium to the following simultaneous move game. Column...
4. Find all of the pure strategy Nash Equilibrium to the following simultaneous move game. Column 15, 8 3,8 9,10 10,6 2 7,4 6,5 3,3 5,0 Row 35,3 3,6 2,7 11,5 47,2 2,3 6,1 10,0 9,0 5 6,4 2,2 12,3
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
Question 5 (25 points). Consider the following simultaneous-move game: Column LIMNIP Ủ11, 1 | 2, 2...
Question 5 (25 points). Consider the following simultaneous-move game: Column LIMNIP Ủ11, 1 | 2, 2 | 3, 4 | 9.3 D12, 5 | 3. 311, 217, 1 Row (a) Find all pure-strategy Nash equilibria. (b) Suppose Row mixes between strategies U and D in the proportions p and (1-p). Graph the payoffs of Column's four strategies as functions of p. What is Column's best response to Row's p-mix? (c) Find the mixed-strategy Nash equilibrium. What are the players' expected...
Please answer 3 Questions, thank you. 4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7)...
Please answer 3 Questions, thank you.
4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7) PLAYER 1 (2,4) (0,6) (2,0) (1,3) (2,4) (0,3) a) Does this game have any pure-strategy Nash equilibrium? If so, identify it (or them) and explain why this is an equilibrium. b) Find a mixed-strategy Nash equilibrium to this game and explain your calculations. Note: a mixed strategy for player i may be expressed by o; = (P1, P2, 1- P1 - p2). c) Is...
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash...
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0)...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0) (-1,0) (-1,1) C (0,1) (1,0) (0,2) (0,2) (0,2) A В (0,2) 1,2) (0,2) (0,2) (0,3) (0,4) (-1,3) (0,3) a. Use the Elimination of Weakly Dominated Strategies Criterion to obtain a solution (unique to the chosen order of elimination) b. Show that the order of elimination matters by finding a different solution (unique to the new chosen order of elimination) c. Show that the solutions...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy Band player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. payoff...
simultaneous move game. Find all equilibrium of this game. Player 2 Left Right Player 1 Left 1, -2...
simultaneous move game. Find all equilibrium of this game. Player 2 Left Right Player 1 Left 1, -2 -1, 2 Right -2, 1 2, -1
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5...
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5 11,0 (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
4. Find all of the pure strategy Nash Equilibrium to the following simultaneous move game. Column 15, 8 3,8 9,10 10,6 2 7,4 6,5 3,3 5,0 Row 35,3 3,6 2,7 11,5 47,2 2,3 6,1 10,0 9,0 5 6,4 2,2 12,3
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
Question 5 (25 points). Consider the following simultaneous-move game: Column LIMNIP Ủ11, 1 | 2, 2 | 3, 4 | 9.3 D12, 5 | 3. 311, 217, 1 Row (a) Find all pure-strategy Nash equilibria. (b) Suppose Row mixes between strategies U and D in the proportions p and (1-p). Graph the payoffs of Column's four strategies as functions of p. What is Column's best response to Row's p-mix? (c) Find the mixed-strategy Nash equilibrium. What are the players' expected...
Please answer 3 Questions, thank you.
4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7) PLAYER 1 (2,4) (0,6) (2,0) (1,3) (2,4) (0,3) a) Does this game have any pure-strategy Nash equilibrium? If so, identify it (or them) and explain why this is an equilibrium. b) Find a mixed-strategy Nash equilibrium to this game and explain your calculations. Note: a mixed strategy for player i may be expressed by o; = (P1, P2, 1- P1 - p2). c) Is...
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
Exercise 2 Consider the following simultaneous move game between two players I II III IV (-2,0) (-1,0) (-1,1) C (0,1) (1,0) (0,2) (0,2) (0,2) A В (0,2) 1,2) (0,2) (0,2) (0,3) (0,4) (-1,3) (0,3) a. Use the Elimination of Weakly Dominated Strategies Criterion to obtain a solution (unique to the chosen order of elimination) b. Show that the order of elimination matters by finding a different solution (unique to the new chosen order of elimination) c. Show that the solutions...
Check my work In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy Band player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. payoff...
2. Consider the following simultaneous move game: Column Left Right Top 1,1 7,3 Row Bottom 3,5 11,0 (a) Find all pure-strategy Nash equilibria (b) Now assume that the game is made sequential with Row moving first. Illustrate this new game using a game tree and find the rollback equilibrium (c) List the strategies of the two players in this sequential-move game and give the normal-form representation of the game (the payoff matrix) (d) Use the payoff matrix to find the...
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