1\2 U D L 4,3 0,0 R 0,0 2,1 Q. Suppose players 1 and 2 play the stage game depicted above. Check whether each of these strategies constitute a SPE? 1. Play U,C in Rounds 1 and 2 2. Play D,R in rounds 1 and 2 each 3. C 1,4 0,0 Play U,L in Round 1 followed by U,C in Round 2. If Player 2 defects punish by playing D,R in round 2. 4. Alternate between U,C and D,R in Rounds 1 and 2

1\2 U D L 4,3 0,0 R 0,0 2,1 Q. Suppose players 1 and 2 play the stage game depicted above. Check whether each of these strategies constitute a SPE? 1. Play U,C in Rounds 1 and 2 2. Play D,R in rounds 1 and 2 each 3. C 1,4 0,0 Play U,L in Round 1 followed by U,C in Round 2. If Player 2 defects punish by playing D,R in round 2. 4. Alternate between U,C and D,R in Rounds 1 and 2

Microeconomics: Principles & Policy

14th Edition

ISBN:9781337794992

Author:William J. Baumol, Alan S. Blinder, John L. Solow

Publisher:William J. Baumol, Alan S. Blinder, John L. Solow

Chapter13: Between Competition And Monopoly

Section: Chapter Questions

Problem 10DQ

See similar textbooks

Similar questions

7. N [0.75] B A [0.25] 1 E F 6 2 J K J K 12 3 9. 6 6. 1 In equilibrium, what is the probability that player 1 will use the pure strategy E in this game?
Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.
2. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" : GMD H 1,2 1,0 1,3 L 2,4 0,0 0,5 and with probability 1/2 the payoffs are according to "Game 2" : G |M|D H 1,2 1,3 1,0 L 2,4 0,5 0,0 (a) Find the Nash Equilibria when neither player knows which game is actually played. (b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game has a unique Bayesian Nash Equilibrium.
please solve it in 30 minute please Consider an infinitely repeated game where the stage game is the game of chicken: Swerve Straight Swerve 0,0 -1,1 Straight 1, –1 -10, -10 Assume that the discount factor is very close to one. For concreteness, you can assume that d = 0.99. (a) Is there an SPE in which player l's payoff is 1/(1 – 6)? Explain. (b) Is there an SPE in which each player gets a payoff of 0? Explain. (c) Is there an SPE in which player l's payoff is -2/(1 – 8)? Explain.
Question 30 Consider the following Extended Form Game: O True A O False (2,3) P1 A' (5,5) A' (3,8) B A P2 B' P2 B' P1 B (1,9) Player 2 threatens to play (A',B') no matter what. Is this threat credible? (9,1)
Consider the following extensive form game between player 1 and player 2. T B (2, 2) L R R (3, 1) (0, 0) (5, 0) (0, 1) (a). Find the normal form representation of this game. (show the bimatrix) (b). Find all pure strategy NE. (c). Which of these equilibria are subgame perfect?
see image Use the following setting for questions 1-3. Consider the following static game: C R L 3,1 0,0 5,0 T M 2,1 1,2 3,1 B 1.2 0,1 4,4 Suppose this game is played for two periods. At the beginning of period 2, the players can observe the outcome from period 1. There is no discounting. 1. First, assume only pure-strategy SPNE such that either player's second period strategy DOES NOT depend on the first period outcome. How many such SPNE are in this game? (a) 1 (b) 2 (c) 3 (d) 4 (e) none 2. Consider only SPNE from the previous question. What is the maximum sum of the players' payoffs that can be achieved in the first period? (a) 0 (b) 3 (c) 4 (d) 5 (e) 8 3. Now consider all possible pure-strategy SPNE such that (B,R) is played in the first period. What must be the equilibrium outcome in the second period of such SPNE? (a) (T,L) (b) (M,C) (c) (B,R) (d) (T,R) (e) There are no such SPNE
し(5,3) b I(2,2) も(0,0) (4,12) a (12.4) (0,0) i). List all subgame pertect Nash equilibria and name one Nash eqvilibrivm that is not subgame pertect i). How many strategies does playot and player 2 have?
A st SW B st 2,1 5, 15 2. Consider the game of chicken above. SW 11,4 3,5 a. Find all Nash equilibrium in pure strategies. b. Say that player A uses a mixed strategy, where she picks st with prob. 0.55 and sw with prob. 0.45. What is B's expected payoffs from choosing pure st and pure sw? c. Player B uses a mixed strategy and wants A to choose sw. What is the minimum prob. p, for which B needs to play st so A will choose sw.
a W 3,5 3,4 8,4 0,0 3,3 8,9 y 0,1 5,9 9,8 Describe a strategy for player 1 that dominates x. O (1/3.0. 2/3) 1.0,0) O01.1) to
5/ Solve the following payoff matrix to find the best strategies and the value of game: BI B2 Al 8 A2 3 5 A3 10 2.
rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.