Chapter 1.4, Problem I.6E

A Concise Intro To Logic

12th Edition

ISBN: 9781305147775

Author: Hurley

Publisher: Cengage

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Chapter 1.4, Problem I.5E

Chapter 1.4, Problem I.7E

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Consider a cheap talk game in which Nature chooses the sender’s type andthere are three feasible types: x, y, and z, which occur with probability 1/4, 1/4,and 1/2, respectively. The sender learns her type and then chooses one of fourpossible messages: m1, m2, m3, or m4. The receiver observes the sender’smessage and chooses one of three actions: a, b, or c. The payoffs are shown in the table below. a. Suppose the sender’s strategy is as follows: (1) if the type is x, thenchoose message m1, and (2) if the type is y or z, then choose messagem2. The receiver’s strategy is the following: (1) if the message is m1,then choose action a; (2) if the message is m2, then choose action b;and (3) if the message is m3 or m4, then choose action a. For appropriatelyspecified beliefs for the receiver, show that this strategy pair is aperfect Bayes–Nash equilibrium.b. Find a separating perfect Bayes–Nash equilibrium.

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