Sender's Receiver's Sender's Receiver's Туре Action Payoff Рayoff a 3 3 b 2 1 2 y a 4 1 y b 5 y 4 a 3 b 1 10 3. 2.
Consider a cheap talk game in which Nature chooses the sender’s type and
there 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, then
choose message m1, and (2) if the type is y or z, then choose message
m2. 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 appropriately
specified beliefs for the receiver, show that this strategy pair is a
perfect Bayes–Nash equilibrium.
b. Find a separating perfect Bayes–Nash equilibrium.
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