Consider a variation of the Glosten-Milgrom sequential trade model where the asset's value V can take three values. Suppose that the true value of stock in Trident Corporation can be, with equal probability, either V H = 3 4 , V L = 1 4 , or some middle value V M . Let = 1 3 of the traders be informed insiders, while the remaining 1 = 2 3 are uninformed noise traders. Assume as always that informed traders always buy when V = V H and sell when V = V L, while uninformed traders buy or sell with equal probability. The focus of this problem is the traders' behavior when V = V M.

Question: Show that there is no value of V M for which informed traders randomize between buying and selling.