Homework Answers
If player 1 goes with the good manufacturing procedure, then the best option for Player 2 is to Buy.
If player 2 goes with the bad manufacturing procedure, then the best option for Player 2 is to Dont buy.
If player 2 goes with Buy, then the best option for Player 1 is to go with the Bad manufcaturing procedure.
If player 2 goes with dont Buy, then the best option for Player 1 is to go with the Bad manufcaturing procedure.
Hence, the nash equilibrium of the game is When Player 1 chooses the bad manufacturing procedure and player 2 chooses dont buy
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2. Consider a Firm (Player 1) that produces a unique kind of drug that is used...
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...
Technology Adoption: During the adoption of a new technology a CEO (player 1) can design a...
Technology Adoption: During the adoption of a new technology a CEO (player 1) can design a new task for a division manager. The new task can be either high level (H) or low level (L). The manager simultaneously chooses to invest in good training (G) or bad training (B). The payoffs from this interaction are given by the following matrix: Player 2 GB 5,4 -5,2 H Player 1 L 2, -2 0,0 a. Present the game in extensive form (a...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
Consider the finite 2 player game, representing price competition in a market where al costumers buy...
Consider the finite 2 player game, representing price competition in a market where al costumers buy from the seller with the lowest price. Both sellers simultaneously choose price, p1 and p2, where pi is in P = {0,1,2,3,4}. The profits to each seller are given in the payoff bi-matrix below, where seller 1 chooses row and seller 2 column. Firm 2 p=0 p=1 p=2 p=3 p=4 p=0 -5,-5 -10,0 -10,0 -10,0 -10,0 p=1 0,-10 0,0 0,0 0,0 0,0 p=2 0,-10...
1. Basic Game Theory (21 points) Consider the following game Player 2 Right 18,25 20.23 Player...
1. Basic Game Theory (21 points) Consider the following game Player 2 Right 18,25 20.23 Player 1 left 20, 24 22. 26 Top Bottom A. (6 points) Docs player 2 have a dominant strategy. If yes, describe it. B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff matrix, find the Nash equilibrium for the...
Consider a game in which, simultaneously, player 1 selects a number x and player 2 select...
Consider a game in which, simultaneously, player 1 selects a number x and player 2 select a number y, where x and y must be greater than or equal to 0. Player 1's payoff is U1 = 8x - 2xy - x2 and player 2's payoff is U2 = 4by + 2xy - y? The parameter b is privately known to player 2. Player 1 knows only that b = O with probability 1/2 and b = 4 with probability...
1. Basic Game Theory (21 points) Consider the following game Player Top Bottom Left 21, 23 22. 16 Player 2 Right 20...
1. Basic Game Theory (21 points) Consider the following game Player Top Bottom Left 21, 23 22. 16 Player 2 Right 20, 24 19. 18 A. (6 points) Does player 2 have a dominant strategy. If yes, describe it B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff matrix, find the Nash equilibrium for...
с 1. Basic Game Theory (21 points) It Consider the following game Player 2 ID Player...
с 1. Basic Game Theory (21 points) It Consider the following game Player 2 ID Player 1 A 20,22 21.24 B 18,23 20.18 f No: no A. (6 points) Does player I have a dominant strategy. If yes, describe it. "Velthen Planchonit in one of B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff...
2. (Cournot Model) Consider a Cournot duopoly. The market demand is p=160 - q2. Firm 1's...
2. (Cournot Model) Consider a Cournot duopoly. The market demand is p=160 - q2. Firm 1's marginal cost is 10, and firm 2's marginal cost is also 10. There are no fixed costs. A. Derive each firm's best response function B. What is the Nash equilibrium of this model? Find the equilibrium market price. C. Find the equilibrium profit for each firm D. Find the equilibrium consumer surplus in this market. 3. (Bertrand Model) Consider a Bertrand duopoly. The market...
QUESTION 15 Consider the following simultaneous-move game: Two firms, Firm 1 (raw player) and Firm 2...
QUESTION 15 Consider the following simultaneous-move game: Two firms, Firm 1 (raw player) and Firm 2 (column player), decide whether to enter (E) or not enter (N) some market. If neither enters, then both make 0. If both enter, the market is oversaturated and so both earn a loss of 5. However, if only one enters, then the entrant earns monopoly profit of 10. Which of the following matrices is the correct representation of the static game? 0.10 10.0 0.0...
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...
Technology Adoption: During the adoption of a new technology a CEO (player 1) can design a new task for a division manager. The new task can be either high level (H) or low level (L). The manager simultaneously chooses to invest in good training (G) or bad training (B). The payoffs from this interaction are given by the following matrix: Player 2 GB 5,4 -5,2 H Player 1 L 2, -2 0,0 a. Present the game in extensive form (a...
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
1. Basic Game Theory (21 points) Consider the following game Player 2 Right 18,25 20.23 Player 1 left 20, 24 22. 26 Top Bottom A. (6 points) Docs player 2 have a dominant strategy. If yes, describe it. B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff matrix, find the Nash equilibrium for the...
Consider a game in which, simultaneously, player 1 selects a number x and player 2 select a number y, where x and y must be greater than or equal to 0. Player 1's payoff is U1 = 8x - 2xy - x2 and player 2's payoff is U2 = 4by + 2xy - y? The parameter b is privately known to player 2. Player 1 knows only that b = O with probability 1/2 and b = 4 with probability...
1. Basic Game Theory (21 points) Consider the following game Player Top Bottom Left 21, 23 22. 16 Player 2 Right 20, 24 19. 18 A. (6 points) Does player 2 have a dominant strategy. If yes, describe it B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff matrix, find the Nash equilibrium for...
с 1. Basic Game Theory (21 points) It Consider the following game Player 2 ID Player 1 A 20,22 21.24 B 18,23 20.18 f No: no A. (6 points) Does player I have a dominant strategy. If yes, describe it. "Velthen Planchonit in one of B. (9 points) Can this game be solved by the elimination of dominated strategy? If yes, describe your method and result in detail C. (6 points) Now suppose there is some change to the payoff...
2. (Cournot Model) Consider a Cournot duopoly. The market demand is p=160 - q2. Firm 1's marginal cost is 10, and firm 2's marginal cost is also 10. There are no fixed costs. A. Derive each firm's best response function B. What is the Nash equilibrium of this model? Find the equilibrium market price. C. Find the equilibrium profit for each firm D. Find the equilibrium consumer surplus in this market. 3. (Bertrand Model) Consider a Bertrand duopoly. The market...
QUESTION 15 Consider the following simultaneous-move game: Two firms, Firm 1 (raw player) and Firm 2 (column player), decide whether to enter (E) or not enter (N) some market. If neither enters, then both make 0. If both enter, the market is oversaturated and so both earn a loss of 5. However, if only one enters, then the entrant earns monopoly profit of 10. Which of the following matrices is the correct representation of the static game? 0.10 10.0 0.0...
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