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Exercise 10.2-4: Cho and Kreps' Intuitive Criterion Consider a PBE and define u(a, 0. ') to be agent I's payoff if he takes the action a off the equilibrium path, his type is 0 and he is believed to be type 0'. Cho and Kreps argue that if Maxrestu, (a, 6, 0')) uf(0). Again consider the worker model of Exercise 10.2-3, but this time there are three types of workers with productivity levels ve = 0, 0 C O = {1, 2, 3). The signaling cost of type 0 is Co(z) = z/0. The three types are equally likely. (a) Show that the set of separating PBE that satisfy the Cho and Kreps' Intuitive Criterion are the education wage pairs ( (z1, wj), (z2, w2), (23, wa)) ={(0, 1), (22, 2), (z2 + 3, 3) } where zz C Zz = [1, 2]. 490 (b) Show that the PBE with only type 3 signaling also satisfies the Cho and Kreps' Intuitive Criterion. (c) Are there other partial pooling equilibria that satisfy the Cho and Kreps' Intuitive Criterion