🤖 AI Summary
This paper addresses the long-standing conceptual ambiguity in quantum game theory by proposing the first axiomatic framework that rigorously distinguishes quantum superposed strategies from entanglement-assisted games. Methodologically, it integrates quantum information theory, axiomatic game theory, operator algebra, and POVM-based measurement modeling to formally characterize quantum players, strategy spaces, quantum measurements, and payoff functions—thereby unifying classical game theory with quantum information structures. The main contributions are: (1) establishing the first empirically verifiable taxonomy of quantum games; (2) providing a rigorous theoretical foundation for designing quantum algorithmic incentive mechanisms, analyzing quantum cryptographic protocols, and modeling quantum multi-agent systems; and (3) revealing its structural potential as a pedagogical tool for teaching quantum knowledge.