2. Apex and Brilliant select prices to maximize their individual profits. The profits are listed in the table below. Apex \ Brilliant Low High (7,0) (4, 4) Low (1, 1) (0, 7) High (i) Find all Nash equilibria of the game. (ii) Now suppose that Apex and Brilliant play the game in (i) an infinite number of periods. The firms discount future payoffs at the rate Sper period, where 0 < 8< 1. Is there a subgame-perfect Nash equilibrium in which both firms select High each period? (iii) Suppose that firms' discount factors change so they are unequal and satisfy 0 < &i < & < 1. Is there a subgame-perfect Nash equilibrium in which both firms select High each period?

2. Apex and Brilliant select prices to maximize their individual profits. The profits are listed in the table below. Apex \ Brilliant Low High (7,0) (4, 4) Low (1, 1) (0, 7) High (i) Find all Nash equilibria of the game. (ii) Now suppose that Apex and Brilliant play the game in (i) an infinite number of periods. The firms discount future payoffs at the rate Sper period, where 0 < 8< 1. Is there a subgame-perfect Nash equilibrium in which both firms select High each period? (iii) Suppose that firms' discount factors change so they are unequal and satisfy 0 < &i < & < 1. Is there a subgame-perfect Nash equilibrium in which both firms select High each period?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.6P

See similar textbooks

Similar questions

Find all Nash equilibria of the following two-player game. Provide necessary computation. L M R A 0,0 в (2,—1| 0,0 C -2,1 | 2, –1 0,0 -2,1 | 2, –1 -2, 1
5. Consider the following Extended Form game where P1 stands for Player one and P2 stands for player two with A, B and A', B' being their respective strategies. A' (1,1) P2 B' (2,3) P1 A' B (4,5) P2 What is the set of Nash Equilibria? Clearly explain your answer. Full-screen Snip B' (6,7)
Consider the following three-Player, extensive-form game - (-2,–1,2) а 2 b 3 Y +(-2,0,0) A (2,0,1) Y 3 (0,0,1) ►(0,0,0) a (0,1,0) (1,1,1) a) Find all pure strategy Nash equilibria of this game. b) Find all pure strategy SPNE of this game.
D Question 11 Consider the following Extended Form Game: O 1 02 O 3 A' 04 (9,5) A P2 P1 B' A' (5,2) (8,5) B x A (1,6) P2 B' According to backwards induction, in how many turn does the game end? P1 B (6,7)
Find the unique Nash equilibrium of a game with the following payoff matrix: Player 2 2 4 1 (6, 7) (13, 8) (9, 9) Player 1 3 (4, 4) (7, 7) (7, 6) (7, 7) (11, 11) (7, 13) О a. (3, 2) O b. (5, 4) О с. (11, 11) O d. (1, 6) O e. There is no unique Nash equilibrium.
• (1,0) (1,1) Player 2 G D H (2,0) Action Player 1 Player 1 Action B Player 1 (3,-1) E Player 2 (0,1) (-1,-1) (a) Find all the Subgame Perfect Nash equilibria in this game. (b) Find all the Nash equilibria in this game. (Hint: write the game in strategic form.)
1. Consider a two player, simultaneous move game. The strategies available to each player and payoffs are shown in the following matrix form: Player 2 C L R 6,4 5,2 8,5 4,4 9,3 5,9 B 7,5 4,4 5,2 Game 5 T Player 1 M a) Find and write down the Nash equilibria in pure strategies, if any exist. b) Say that instead of being a simultaneous move game this game had been sequential. First player 1 will choose a strategy and then player 2 will observe the choice made by player 1 and choose a strategy. The full structure of the game, including all payoffs, is common knowledge to both players. Sketch a game tree to represent the extensive form of this game. Find and write down the subgame perfect Nash equilibria.
q52 If you advertise and your rival advertises, you each will earn 14 million in profits. If neither of you advertises, you will each earn 20 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn 10 million and the non-advertising firm will earn 16 million. If you and your rival plan to be in business for only one year, the Nash equilibrium is a. for each firm to advertise. b. for the other firm to advertise and your firm not to advertise. c. for your firm to advertise and the other not to advertise. d. for neither firm to advertise.
Consider a Centipede game below. Player 1 moves first and he can choose either L or R. If player 1 chooses R; then Player 2 moves choosing either L or R and if he chooses R then Player 1 moves choosing either L or R and then finally player 2 moves. 1 R 2 R 1 R 2 R 9,9 L 2,0 0,4 6,2 4,8 a. Represent this game in a normal form b. Find all the Pure Strategy Nash equilibrium or equilibria c. Find all the Sub-game Perfect Nash Equilibrium of this game
QS. Consider the following stage game B. C A (4, 4) (1, 5) (0, 3) B (7, 1) (3, 4) (0, 1) C (3, 0) (2, 0) (1, 1) (a). Find all Nash equilibria of the stage game (b). Suppose that the stage game is played two times and with agents discount factor given by 0<6 <1. Is there a subgame perfeet equilibrium equilibrium strategy profile in which (A, A) is played in the first round? If not explain whv. (Hint: Think of o 1)
Question 5 Consider the following Extended Form Game: A' (1,1) A P2 B' O [(B, B')} (2,3) O ((B.(B',A')). (B.(B¹, B'))) P1 A' What is the set of Nash Equilibria? O {(B.(A', B)), (B,(B', B'))) (4,5) B O ((B.(A'A')). (B.(A, B')). (B,(B,A')), (B,(B', B'))} P2 B' (6,7)
Consider the two period Repeated Prisoner's Dilemma Game where each player is interested in the SUM of the payoffs she gets in each period. Players see the outcome after the play in each period. (The period payoffs are 10,5,1,0.) (i) Write out this game in its strategic form. (ii) Find all Nash equilibria and all Subgame Perfect Nash Equilibria.