Ex #2. (Problem #2) Consider the cheap talk model with the following conditions: only takes values...

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Ex #2. (Problem #2) Consider the cheap talk model with the following conditions: only takes values of the form , where n is a fixed integer, and k is an integer such that 0 k n. That is, takes values ,-1,1}. The receiver believes that each possible value of has equal in the set {0,1,2, probability, i.e. is uniformly distributed on the set of possible values. (a) Show that there is an equilibrium where the sender perfectly reveals the state if and only if b (If you are not able to answer this, you may focus on the case where n = 6.) n b) Suppose that n = 6 and > Construct a partitional equilibrium: That is, an equi- librium with an integer k* k*. c) Can you modify you construction in (b) so that you have a partitional equilibrium with three subsets? Ex #2. (Problem #2) Consider the cheap talk model with the following conditions: only takes values of the form , where n is a fixed integer, and k is an integer such that 0 k n. That is, takes values ,-1,1}. The receiver believes that each possible value of has equal in the set {0,1,2, probability, i.e. is uniformly distributed on the set of possible values. (a) Show that there is an equilibrium where the sender perfectly reveals the state if and only if b (If you are not able to answer this, you may focus on the case where n = 6.) n b) Suppose that n = 6 and > Construct a partitional equilibrium: That is, an equi- librium with an integer k* k*. c) Can you modify you construction in (b) so that you have a partitional equilibrium with three subsets?