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This paper proposes a Cournot model that can be used to analyze the strategic behaviors of generation companies which try to maximize their profits in an imperfectly competitive electricity and carbon markets. The proposed model consists of two parts. First, the strategic behaviors of generation companies are modeled based on the Cournot theory. Second, the market operation is modeled based on the assumption that the market operator tries to maximize the total social welfare in consideration of environmental welfare. To find the Nash equilibrium of the proposed model, the two-level optimization technique is used. The proposed method has been applied to an illustrative example of oligopolistic markets. We found that the proposed method has strong potential to analyze the influence of the strategic biddings of the generation companies and the impact of renewable generator on markets where the competitiveness of the markets is not fully developed.