Quantum Games and the Relationships between Quantum Mechanics and Game Theory

Abstract: Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum domain where the linear superposition of actions is allowed. This quantization let us describe and solution problems originated by conflicting or cooperative behaviors among the members of a system from the point of view of quantum mechanical interactions. This leads us to interesting aspects which only can be observed through the quantization of a game like the possibility of the entanglement between players, the definition of a socioeconomical temperature in a system, the collective welfare principle,the analysis of a game through elements of quantum information theory and the globalization process. The relationships between quantum mechanics and game theory are also studied and its shown how although both systems analyzed are described through two theories apparently different (quantum mechanics and game theory) both are analogous and thus exactly equivalents.