Quantum game theory enhances classical game theory through the integration of principles from quantum physics and is experiencing rapid development. Quantum networks, utilizing entanglement, possess the capability to transform communication and distributed computing. Efficient distribution of entanglement across quantum nodes (Q-nodes) is essential for the optimization of network performance. This study presents a new resource allocation strategy for quantum networks, utilizing principles from quantum game theory. In a competitive or cooperative quantum environment, Q-nodes utilize quantum strategies to accomplish either individual or collective objectives. Each Q-node initiates a request for entanglement resources, while the system models interactions in the form of a quantum game. Quantum measurements determine payoffs by employing the principles of superposition and entanglement. The proposed method dynamically allocates resources based on game outcomes to optimize entanglement distribution. Convergence occurs when the allocation of resources stabilizes as a result of iterative processes. This framework enhances the performance of both nodes and systems, providing benefits compared to traditional methods. Applications encompass quantum communication, cryptography, and distributed computing.