In the rapidly advancing era of 6G networks, an efficient resource allocation (RA) is necessitated. Consequently, our paper reveals a sophisticated mathematical model based on Evolutionary Game Theory and replicator dynamics, designed to optimize and stabilize resource distribution. The model delineates how Evolutionary Stable Strategies (ESS) can be systematically identified and employed to enhance network efficiency and fairness significantly. Further, the integration of strategic interaction analysis and dynamic modelling demonstrates that ESS not only
respond adeptly to changing network conditions but also robustly guard against inefficiencies caused by signal degradation and user demand variability. Our empirical simulations validate the
model’s effectiveness in fostering resilient and equitable RA, thereby setting a foundation for future 6G network designs that prioritize adaptability and sustainability. Furthermore, we
proposed a few algorithms, such as ESS sustainability and stabilization criteria for ESS, to depict the change in strategy population, which turns into the strategy fitness change and
convergence of strategic population, respectively. Moreover, our paper aims to highlight the innovative approach succinctly, additionally, the theoretical foundation and practical outcomes
of our research, focusing to engage and address a wider audience effectively in the upcoming era of next-generation communication technologies.

Evolutionary Stable Strategies,6G,Resource allocation,Evolutionary game theory