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Questions 10, and 11 refer to this game: ont Sonia Move 1 Move 2 Yuhan Move...
6. If a single strategy is always optimal, regardless of opponents' strategies, then it is a...
6. If a single strategy is always optimal, regardless of opponents' strategies, then it is a a. First-mover advantage b. A Nash equilibrium c. Prisoners Dilemma d. A dominant strategy 7. In a market with a monopolist, which of the following pricing strategies maximizes total social welfare (no deadweight loss)? a. Perfect price discrimination b. Block pricing C. Group price discrimination d. None of the above; all monopolist pricing strategies create a deadweight loss Questions 8, and 9 refer to...
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...
MCS 11. The figure to the right shows the market with a negative externality. The competitive...
MCS 11. The figure to the right shows the market with a negative externality. The competitive equilibrium quantity is a. A b. B c. C d. D 12. The figure to the right shows the market with a negative externality. The monopoly equilibrium quantity is a. A b. B MR -MCP P(Q) AB C D Q C. C d. D 13. A pure public good is a. A good that the public must pay for b. Non rival in consumption...
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...
2. Consider the following simultaneous move game: Column Left Right 1,1 3,5 11,0 Тoр 7,3 Row...
2. Consider the following simultaneous move game: Column Left Right 1,1 3,5 11,0 Тoр 7,3 Row Bottom (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...
2. Consider the following simultaneous move game Column Left Right 1.1 7,3 3.5 Тор Row Bottom...
2. Consider the following simultaneous move game Column Left Right 1.1 7,3 3.5 Тор Row Bottom 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...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2,...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2, 2) (2, 2) (0, 6) (6, 0 (0,0 (6, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy Bayesian Nash equilibrium (equilibria) b) Find pure strategy subgame perfect equilibrium (or equilibria) of this game. c) Find pure strategy perfect Bayesian equilibrium (or equilibria) of this game.
8. In a market with a monopoly that faces direct demand Q(P) = a - bP,...
8. In a market with a monopoly that faces direct demand Q(P) = a - bP, and cost function c(Q) dQ - eQ? then the firm's marginal revenue function is a. b b C. MCS MR -MCP b. a- a-2bQ d. none of the above 9. The figure to the right shows the market with a negative externality. The competitive equilibrium quantity is a. A b. B c. C d. D 10. The figure to the right shows the market...
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
3. Player 1 and Player 2 are going to play the following stage game twice: &n...
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
6. If a single strategy is always optimal, regardless of opponents' strategies, then it is a a. First-mover advantage b. A Nash equilibrium c. Prisoners Dilemma d. A dominant strategy 7. In a market with a monopolist, which of the following pricing strategies maximizes total social welfare (no deadweight loss)? a. Perfect price discrimination b. Block pricing C. Group price discrimination d. None of the above; all monopolist pricing strategies create a deadweight loss Questions 8, and 9 refer to...
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...
MCS 11. The figure to the right shows the market with a negative externality. The competitive equilibrium quantity is a. A b. B c. C d. D 12. The figure to the right shows the market with a negative externality. The monopoly equilibrium quantity is a. A b. B MR -MCP P(Q) AB C D Q C. C d. D 13. A pure public good is a. A good that the public must pay for b. Non rival in consumption...
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...
2. Consider the following simultaneous move game: Column Left Right 1,1 3,5 11,0 Тoр 7,3 Row Bottom (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...
2. Consider the following simultaneous move game Column Left Right 1.1 7,3 3.5 Тор Row Bottom 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...
3. General Extensive Form Game D Suppose the following general extensive form game 1/2 1/2 (2, 2) (2, 2) (0, 6) (6, 0 (0,0 (6, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy Bayesian Nash equilibrium (equilibria) b) Find pure strategy subgame perfect equilibrium (or equilibria) of this game. c) Find pure strategy perfect Bayesian equilibrium (or equilibria) of this game.
8. In a market with a monopoly that faces direct demand Q(P) = a - bP, and cost function c(Q) dQ - eQ? then the firm's marginal revenue function is a. b b C. MCS MR -MCP b. a- a-2bQ d. none of the above 9. The figure to the right shows the market with a negative externality. The competitive equilibrium quantity is a. A b. B c. C d. D 10. The figure to the right shows the market...
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
3. Player 1 and Player 2 are going to play the following stage
game twice:
Player 2
Left
Middle
Right
Player 1
Top
4, 3
0, 0
1, 4
Bottom
0, 0
2, 1
0, 0
There is no discounting in this problem and so a player’s payoff
in this repeated game is the sum of her payoffs in the two plays of
the stage game.
(a) Find the Nash equilibria of the stage game. Is (Top, Left) a...
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