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This paper is devoted to the problem of obtaining class probability estimates for multi-class classification problem in Error-correcting output coding (ECOC) framework. We consider the problem of class prediction via ECOC ensemble of binary classifiers as a decision-making problem and propose to solve it using game theory approach. We show that class prediction problem in ECOC framework can be formulated as a matrix game of special form. Investigation of the optimal solution in pure and mixed strategies is resulted in development of novel method for obtaining class probability estimates. Experimental performance evaluation on well-known benchmark datasets has demonstrated that proposed game theoretic method outperforms traditional methods for class probabilities estimation in ECOC framework.