The growing use of machine learning algorithms in decisions that significantly affect people necessitate interpretable and fair approaches. Mathematical programming based machine learning models have attracted attention because of the flexibility they provide to integrate features like interpretability and fairness, combined with high accuracy. This work introduces a mathematical programming based classification tree that uses a game theoretic approach to address group fairness. The proposed mathematical formulation is a Mixed Integer Linear Programming model using a piecewise linearisation strategy based on special-ordered sets. The overall misclassification rate is the fairness metric examined and the Nash bargaining scheme is followed to balance the trade off between the misclassification error of the groups. The efficiency of the methodology is evaluated via three binary and multi-class literature datasets, which provide evidence for the fairness and accuracy of the predictions made by the model.