The paper considers a new method of the spectrum scheduling process and QoS support in distributed wireless networks using a game theoretic-framework. The game uses incomplete information model, so the concept of the Bayesian Nash equilibrium is used. Moreover, we consider the new algorithm of distributed spectrum sharing based on the Cournot oligopoly competition. Multiple traffic classes of high and low priority have been used with special parameters which represent priority classes and the volume of users' individual demands. The proposed resource-sharing algorithm may be used in distributed opportunistic or cognitive wireless networks.