2. Consider a cheap talk game in which Nature moves by choosing a sender's type, where the type space has four elements: −1, 1, 2, and 3, each occur- ring with equal probability of 1½. The sender learns his type and chooses one of three possible messages: bumpy, smooth, and slick. The receiver observes the sender's message and then chooses one of three actions: 0, 5, and 10. The sender's payoff equals his type multiplied by the receiver's action. The receiver's payoff equals the sender's type multiplied by twice the receiver's payoff. a. Find a separating perfect Bayes-Nash equilibrium. b. Find a semiseparating perfect Bayes-Nash equilibrium.
2. Consider a cheap talk game in which Nature moves by choosing a sender's type, where the type space has four elements: −1, 1, 2, and 3, each occur- ring with equal probability of 1½. The sender learns his type and chooses one of three possible messages: bumpy, smooth, and slick. The receiver observes the sender's message and then chooses one of three actions: 0, 5, and 10. The sender's payoff equals his type multiplied by the receiver's action. The receiver's payoff equals the sender's type multiplied by twice the receiver's payoff. a. Find a separating perfect Bayes-Nash equilibrium. b. Find a semiseparating perfect Bayes-Nash equilibrium.
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
Chapter18: Auctions
Section: Chapter Questions
Problem 18.1IP
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Transcribed Image Text:2. Consider a cheap talk game in which Nature moves by choosing a sender's
type, where the type space has four elements: −1, 1, 2, and 3, each occur-
ring with equal probability of 1½. The sender learns his type and chooses
one of three possible messages: bumpy, smooth, and slick. The receiver
observes the sender's message and then chooses one of three actions: 0, 5,
and 10. The sender's payoff equals his type multiplied by the receiver's
action. The receiver's payoff equals the sender's type multiplied by twice
the receiver's payoff.
a. Find a separating perfect Bayes-Nash equilibrium.
b. Find a semiseparating perfect Bayes-Nash equilibrium.
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