2. Consider the stock recommendation game from lecture. An analyst can only observes a state from the set A={O,N,U} with Pr(O)=Pr(N)=Pr(U)=1/3, and he can make a recommendation, Buy (B), Hold (H) or Sell (S) for an investor. After hearing the analyst's recommendation, the investor can choose Buy (B), Hold (H) or Sell (S). The investor earns 1 if he chooses B given state O,H given state N, and S given state U, and 1 if he chooses S given state O, 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 b when she sells, where let a,b>0. (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. (c) Show whether there exists a partially separating equilibrium such that [m(O)= B,m(N)=B,m(U)=S] for some values of a and b. If so, specify the range for a and b. 2. Consider the stock recommendation game from lecture. An analyst can only observes a state from the set A={O,N,U} with Pr(O)=Pr(N)=Pr(U)=1/3, and he can make a recommendation, Buy (B), Hold (H) or Sell (S) for an investor. After hearing the analyst's recommendation, the investor can choose Buy (B), Hold (H) or Sell (S). The investor earns 1 if he chooses B given state O,H given state N, and S given state U, and 1 if he chooses S given state O, 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 b when she sells, where let a,b>0. (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. (c) Show whether there exists a partially separating equilibrium such that [m(O)= B,m(N)=B,m(U)=S] for some values of a and b. If so, specify the range for a and b