Consider the model of cheap talk discussed in the lectures, with the following difference:
θ only takes values of the form k/n, where n is a fixed integer, and k is an integer such that 0 <= k <= n. That is, θ takes values in the set {0, 1/n, 2/n, . . . , (n-1)/n, 1}. The receiver believes that each possible value of θ has equal probability, i.e. θ 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 <= 1/2n. (If you are not able to answer this, you may focus on the case where n = 6).
(b) Suppose that n = 6 and 1/n > b > 1/2n. Construct a partitional equilibrium: that is, an equilibrium with an integer k* < n, where the sender only discloses whether k < k* or k >= k*.