2. Consider the stock recommendation game from lecture. An analyst can only observes a state from the set 8,; = {0, N, U} with Pr (0) = Pr (N) = Pr (U) = 1/3, and he can make a recommendation, Buy (B), Hold (H) or Sell (8) for an investor. After hearing the analyst's recommendation, the investor can choose Buy (B), Hold (H) or Sell (3) The investor earns 1 if he chooses B given state 0, H given state N, and 8 given state U, and 1 if he chooses 3 given state 0, and B given state U. His payoff is 0 for all other cases. The analyst's payoff equals the investor's payoff plus a. when the investor buys, and less 5 when she sells, where let (1,6 > U. (a) Show whether there exists a pooling equilibrium such that [m(O) : S, m(N) = S, m(U) = S]. (b) Explain carefully whether the following statement is true or not: in a cheap talk game, any pooling equilibrium exists. ((3) Show whether there exists a partially separating equilibrium such that [m (0) : B, m (N) = B, m (U) = S] for some values of a and b. If so, specify the range for a and b