Consider a cheap talk signaling game. The state of the world is ω

= 1 or 2. Each state is equally likely. In the game, Expert E learns the exact state. Then E sends a message m to the Decider D, where m is one of the possible values of ω. After hearing the message, D chooses a policy p, which is a number (any number is a possible policy). D’s utility is −|p − ω|, and E’s utility is −|p − ω − 1|. So, D wants policy p = ω, but E wants p = ω + 1.

-(a) Suppose E uses a separating strategy: send m = 1 if ω = 1, and sendm=2ifω=2. WhatpolicydoesDimplementafterm=1 and m = 2?
-(b) Given how D responds to each message, does E prefer to send m = 2 when ω = 2, or is m = 1 better?
-(c) Given how D responds to each message, does E prefer to send m = 1 when ω = 1, or is m = 2 better?
-(d) Is there a PBE in which E uses this messaging strategy?
-(e) Consider a cheap talk game exactly like the previous problem,except ω=1or20. Is it aBNE for E to send m=1 if ω = 1, and m = 20 if ω = 20?

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