Abstract
This paper explores a game-theoretic model for task allocation in distributed systems, where processors with varying speeds and external load factors are considered strategic players. The goal is to understand the impact of processors' strategic behaviors on workload management and overall system efficiency, focusing on the attainment of a pure strategy Nash Equilibrium (NE). The research rigorously develops a formal mathematical model and validates it through extensive simulations, highlighting how NE ensures stability but may not always yield optimal system performance. The adaptive algorithms for dynamic task allocation are proposed to enhance efficiency in real-time processing environments. Results demonstrate that while NE provides stability, the adoption of optimal cooperative strategies significantly improves operational efficiency and reduces transaction costs. The findings contribute valuable insights into the strategic interactions within computational frameworks, offering guidelines for developing more efficient systems. This study not only advances the theoretical understanding of strategic task allocation but also has practical implications for system design and policy-making in areas such as cloud computing and traffic management.