3. Consider the game below. С1 C2 C3 4, 6 1, 1 7, 6 R1 5, 4 R2 8, 5 2, 6 R3 1, 2 0,7 2, 7 3.1. Does the game have any pure strategy NEs? 3.2. Check whether a mixed strategy NE exists in which A is mixing R1 and R2 with positive probabilities, playing R3 with zero probability, while B is mixing C1 and C3 with positive probabilities while playing C2 with zero probability. [Let (p1, P2, P3) be the probabilities with which A plays (R1, R2,R3) and let (q1, 92, 93) be the probabilities with which B plays (C1, C2,C3). Make use of the following NE test: m* is a NE if for every player i, u¿(m² , m_;) = u;(si, m²¡) for every sį E Si|m¡(sji) > 0 and u¡(m¡ ,m²¡) > u¡(s¡,m;) for every si E Si |m¡ (s¡) = 0. Hint: Each player must be indifferent between those of her pure strategies that are used (with positive probability) in her mixed strategy, and unused strategies must not yield a payoff that is higher than the payoff a player gets with her NE (mixed) strategy.] %3D

3. Consider the game below. С1 C2 C3 4, 6 1, 1 7, 6 R1 5, 4 R2 8, 5 2, 6 R3 1, 2 0,7 2, 7 3.1. Does the game have any pure strategy NEs? 3.2. Check whether a mixed strategy NE exists in which A is mixing R1 and R2 with positive probabilities, playing R3 with zero probability, while B is mixing C1 and C3 with positive probabilities while playing C2 with zero probability. [Let (p1, P2, P3) be the probabilities with which A plays (R1, R2,R3) and let (q1, 92, 93) be the probabilities with which B plays (C1, C2,C3). Make use of the following NE test: m* is a NE if for every player i, u¿(m² , m_;) = u;(si, m²¡) for every sį E Si|m¡(sji) > 0 and u¡(m¡ ,m²¡) > u¡(s¡,m;) for every si E Si |m¡ (s¡) = 0. Hint: Each player must be indifferent between those of her pure strategies that are used (with positive probability) in her mixed strategy, and unused strategies must not yield a payoff that is higher than the payoff a player gets with her NE (mixed) strategy.] %3D

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

1) Given the following payoffloss table for a game between two players: Player 2 (Defensive) Strategies A B C Player 1 (Offensive) Strategies a) What type of game do the two players play? Determine the range of the value of the game. b) Determine the probability of the strategies of each player. c) What strategies should the two players play? What is the value of the game? Who wins the game?|| 1 2 6 -1 2 5 4 3 1 -2 -2
11. What are the subgame perfect equilibria of the following game? Out In T B 7,21 L R L/R 9,3 1,1 1,1 3,9 (a) (InT, L), (OutB, R) and (OutT+OutB, L + R). (b) (InT, L) and (OutB, R). (c) Out and (InT, L). (d) (InT, L), (OutB, R) and (OutT+OutB, L + R). (e) (InT, L). 2
2. Consider a two-stage game of complete but imperfect information where players 1 and 2 simultaneously choose actions a₁ and a₂ in stage 1 and players 3 and 4 simultaneously choose actions a3 and a in stage 2. Provide the notation for the Nash equilibrium in stage 2. How come players 1 and 2 can anticipate this outcome in stage 2?
3. Find ALL Nash equilibria of the following game: Nature begins by choosing one of the 2x2 games. It chooses the left game with probability a, and the right game with probability 1- a. Player 2 is INFORMED about nature's choice but player 1 IS NOT informed. L KR R 0,0| 5, 0,0 U 2, 2 0, 3 U D 3, 1, 1 D 1 Are there values of a for which there exists a mixed strategytequilibrium?
3
For the game given, use the best-reply method to find the Nash equilibria.
Peter X O a. 3 O b. 2 O c. more than 3 O d. 1 O e. none Y Z R 9,6 6,6 9,7 How many (pure strategy) Nash equilibria does this game have? Sarah S 4,4 7,6 1,5 T 6,-3 2,2 6,7
Consider the following game A 1.0 2. 0 0,0 3,3 3.4 0,2 2.4 5.2 p.1 How many Nash equilibria in pure strategies does this game have? F園 OA O OB1 OC2 O D.3 O E. More than 3
2. Consider the following two player game in normal form: Player 2 R 0, 5 2, 3 2, 3 Player 1 M 2, 3 0, 5 3, 2 B 5,0 3, 2 2, 3 (a) Show that for Player 1, strategy T is strictly dominated by a mixed strategy in which actions M and B are played with positive probability. (b) Find a mixed strategy Nash equilibrium of this game. 352
Asap
Q2 Hand written plz Find any Nash equilibria in the following normal form game and indicate which Nash equilibria, if any, are strict. Player 2 b a W 3,5 1, -3 Player 1 x 2,-4 1,2 5,2 1, 1 7,1 5,2 Y 2 d C 2,5 -1,4 3,4 0,3 -2,5 3,2 0,2 3,2
Question 28 Suppose the following game: I Player 1 nice nice Player 2 50, 50 mean 90,20 Which of the following is true? mean 20,90 30, 30 O Both players play "mean" with a 70 % chance, and "nice" with a 30% chance. O There is no Nash Equilibrium in pure strategies, there is only one Nash Equilibrium in mixed strategies. Both players play "nice" with a 70% chance, and "mean" with a 30% chance. There is no Nash Equilibrium in mixed strategies, there is only one Nash Equilibrium in pure strategies.