1. Consider the cheap talk game between the expert and the president, which we discussed in class. That is, we consider a signaling game with $N = \{1, 2\}$, $\Theta = M = A = \{x, y\}$, $p(x) = \frac{1}{3}$. The payoffs for the president (player 2) are the same as those defined in class. However, we now assume the payoffs for the expert (player 1) is such that he wants not to match the president's policy with the state of the world:
$v_1(m, a; \theta) = \begin{cases} 0 & \text{if } a = \theta, \\ 1 & \text{if } a \neq \theta. \end{cases}$
Prove that there is no perfect Bayesian equilibrium in which $s_1(x) = x$ and $s_1(y) = y$.
