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

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter16: Bargaining

Section: Chapter Questions

Problem 3MC

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