Millions of people worldwide are afflicted with skin cancer every year. It happens when DNA damage from UV radiation from the sun or tanning beds causes skin cells to proliferate out of control. Skin lesion analysis is one of the many medical imaging jobs where computer vision models are widely used. Convolutional Neural Networks (CNNs), in particular, are deep learning models that have demonstrated proficiency in extracting pertinent information from images and offer high accuracy in classification tasks. In order to train several CNN models simultaneously on a dataset, this work suggests a novel non-cooperative game theory-based method that involves forcing the models to compete with one another. The interaction between the models not only improves their overall performance, but also underscores the efficiency of our approach in optimizing training time. This approach is evaluated on two publicly available skin lesion datasets, namely HAM10000 dataset for multi-class classification yielding 92.93% accuracy, and PH2 for binary class classification achieving 99.88% accuracy. The code of the proposed methodology can be found at: GitHub repository .