Unlike previous literature, in which firms compete in the market with the same information, this article analyses a two-period duopoly game in which only one firm is completely informed about the market conditions, whereas the other firm is unaware of one parameter of the demand curve. In this setting, we describe how the informed firm uses its price set in period 1 in order to reveal or to hide its private information and how the uninformed firm uses its own price in period 1 in order to learn the market conditions when they are not revealed by its rival. Specifically, we obtained the conditions under which the informed firm sets a higher price than its short-run optimum in the first period to hide its private information in certain cases and to reveal that information in others. Likewise, this paper describes the conditions under which the uninformed firm sets a lower price than its short-run optimum in period 1 in order to learn the unknown parameter. We found that the informed firm´s cost of revealing its private information to its rival is lower than the uninformed firm´s cost of learning the market conditions.