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The presented study models market behavior strategies for firms in real (“impure”) markets.Aim. The presented study aims to develop tools for optimizing (according to the criterion of profit maximization) the market behavior of firms based on the achievements of modern mathematics.Tasks. The authors describe theoretical approaches to modeling the behavior of firms; define the problem of modeling the market behavior of firms in the language of game theory; modify the game model by implementing elements of the theory of fuzzy logic and fuzzy sets; develop and test a methodological approach to identifying the optimal behavior of firms based on fuzzy game modeling.Methods. This study uses general methods of economic and mathematical modeling, provisions of neoclassical and institutional firm theory, tools of game theory and the theory of fuzzy logic and fuzzy sets.Results. The optimal market behavior strategy for firms selling the same product is determined. The implementation of this strategy focuses on maximizing profits with allowance for the imperfections of real markets. A rigorous solution to this problem is proposed, based on the provisions of game theory, theory of fuzzy sets and fuzzy logic. The developed methodological approach to identifying the optimal market behavior strategy based on fuzzy game modeling is illustrated by a meaningful example.Conclusions. The developed and tested methodological approach to identifying the optimal market behavior strategy based on fuzzy game modeling described in the article allows firms to search for optimal strategies with allowance for the imperfections of real markets. It can be used for theoretical modeling of the behavior of firms in an “impure” market, including in a mixed economy, where the government has a certain degree of planning and administrative influence on economic processes. The proposed approach can be recommended for use by the management of firms in the development and implementation of competitive strategies.