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"Cognitive radio" is an emerging technique to improve the utilization of radio frequency spectrum in wireless networks. In this paper, we consider the problem of spectrum sharing among a primary user and multiple secondary users. We formulate this problem as an oligopoly market competition and use a Cournot game to obtain the spectrum allocation for secondary users. Nash equilibrium is considered as the solution of this game. We first present the formulation of a static Cournot game for the case when all secondary users can observe the adopted strategies and the payoff of each other. However, this assumption may not be realistic in some cognitive radio systems. Therefore, we formulate a dynamic Cournot game in which the strategy of one secondary user is selected solely based on the pricing information obtained from the primary user. The stability condition of the dynamic behavior for this spectrum sharing scheme is investigated.