Federated Learning (FL) has gained prominence as a decentralized machine learning paradigm, allowing clients to collaboratively train a global model while preserving data privacy. Despite its potential, FL faces significant challenges in heterogeneous environments, where varying client resources and capabilities can undermine overall system performance. Existing approaches primarily focus on maximizing global model accuracy, often at the expense of unfairness among clients and suboptimal system efficiency, particularly in non-IID (non-Independent and Identically Distributed) settings. In this paper, we introduce FLamma, a novel Federated Learning framework based on adaptive gamma-based Stackelberg game, designed to address the aforementioned limitations and promote fairness. Our approach allows the server to act as the leader, dynamically adjusting a decay factor while clients, acting as followers, optimally select their number of local epochs to maximize their utility. Over time, the server incrementally balances client influence, initially rewarding higher-contributing clients and gradually leveling their impact, driving the system toward a Stackelberg Equilibrium. Extensive simulations on both IID and non-IID datasets show that our method significantly improves fairness in accuracy distribution without compromising overall model performance or convergence speed, outperforming traditional FL baselines.