  In a very simple stock market, made by only two \emph{initially equivalent}
traders, we discuss how the information can affect the performance of the
traders. More in detail, we first consider how the portfolios of the traders
evolve in time when the market is \emph{closed}. After that, we discuss two
models in which an interaction with the outer world is allowed. We show that,
in this case, the two traders behave differently, depending on \textbf{i)} the
amount of information which they receive from outside; and \textbf{ii)}the
quality of this information.
