Consider the simple version of the model of Glosten \& Milgrom [790] described in Sect. 10.3, where the fundamental value \(\tilde{v}\) of the asset is a random variable taking the two possible values \(\bar{v}\) and \(\underline{v}\) with probabilities \(\pi\) and \(1-\pi\), respectively, and where the probability that an agent is informed is \(\alpha\). Suppose furthermore that an uninformed agent is equally likely to submit a buy or a sell order. By making use of Bayes' rule, show that the equilibrium bid and ask prices set by the dealer by applying the zero expected profits condition are explicitly given as in (10.28).