Gibbons 4.9

4.9. Consider the example of Crawford and Sobel's cheap-talk model discussed in Section 4.3.A: the Sender's type is uniformly distributed between zero and one (formally, T = [0, 1] and p(t) = 1 for all t in T); the action space is the interval from zero to one (A = [0, 1]); the Receiver's payoff function is UR(t, a) = -(a - t)2; and the Sender's payoff function is Us(t, a) = -[a - (t + b)]. For what values of b does a three-step equilibrium exist? Is the Re- ceiver's expected payoff higher in a three- or a two-step equi- librium? Which Sender-types are better off in a three- than in a two-step equilibrium?4.3. a. Specify a pooling perfect Bayesian equilibrium in which both Sender types play R in the following signaling game