Quantum Approach to Game Theory

Taksu Cheon

Wenjie Liu, Jingfa Liu, Mengmeng Cui +1 more

With utilizing some quantum mechanism into the game theory, quantum game theory provides us with the ability to achieve results not otherwise possible. In this paper, a brief overview of classical game theory and some game-theoretic terms are depicted. Then, an introduction to quantum theory is presented as well as some correlative works in this field. Finally, some well-known quantum games are analyzed and discussed, which shows its predominant effect on some games problems (the Prisoners' Dilemma, Parrondo's Games, etc.).

Indranil Ghosh

Faisal Shah Khan, Simon J. D. Phoenix

In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of "quantized games", and of applying game theory to quantum mechanics, referred to henceforth as "gaming the quantum", have become synonymous under the single ill-defined term "quantum game". Here, these two perspectives are delineated and a game-theoretically proper description of what makes a multi-player, non-cooperative game quantum mechanical, is given. Within the context of this description, finding a Nash equilibrium in a strictly competitive quantum game is shown to be equivalent to finding a solution to a simultaneous best approximation problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of "equilibrium" behavior of quantum physical systems such as those utilized in quantum information processing and computation.

Indranil Ghosh

Faisal Shah Khan, Simon J. D. Phoenix

In the time since the merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of ``quantized games'', and of applying game theory to quantum mechanics, referred to henceforth as ``gaming the quantum'', have become synonymous under the single ill-defined term ``quantum game''. Here, these two perspectives are delineated and a game-theoretically proper description of what makes a multiplayer, non-cooperative game quantum mechanical, is given. Within the context of this description, finding Nash equilibrium in a zero-sum quantum game is exhibited to be equivalent to finding a solution to a simultaneous distance minimization problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of ``equilibrium'' behavior of quantum physical systems such as those utilized in quantum information processing and computation.