Mathematical Transformations in Game Theory: Wavelet vs. Fourier Transforms

Abstract

This paper explores the intersection of game theory and mathematical transformations, specifically wavelet and Fourier transforms. We examine the foundational principles of game theory and introduce the mathematical bases of wavelet and Fourier transforms. By comparing these transformations, we uncover their unique strengths in enhancing game theoretical models. Wavelet transforms excel in dynamic, multi-scale scenarios due to their localization properties, while Fourier transforms are effective in periodic, stationary environments. Our analysis highlights the complementary nature of these transforms, proposing hybrid approaches for optimizing strategies and predicting outcomes in complex games. This study underscores the potential for interdisciplinary research to advance strategic decision-making.