Quantum Prisoner's Dilemma Model For Collective Dephasing Noise Channel

Since Meyer introduced the quantum strategy to solve the coin flipping problem in 1999,modern game theory has entered the era of the quantum game.Because it can solve many problems that classical games cannot solve,it has attracted extensive attention from many scholars at home and abroad.But most is about the theory of quantum game theory research is carried out under the condition of a closed quantum system,in fact,a completely closed quantum system only exists in the ideal,in the real conditions,any quantum systems,and environment in a certain degree of coupling,it is hard to avoid,so the open quantum systems under the nature of the game Nash equilibrium,it is crucial for the further development of quantum game theory.In quantum transport,collective-dephasing noise is one of the most common quantum noises describing the external environment,and the prisoner's dilemma is one of the most important models in classical game models.In this thesis,the prisoner's dilemma game model is quantized by using MW(Marinatto and Weber)quantization scheme.By introducing collective-dephasing noise into the quantum prisoner's dilemma,the Nash equilibrium strategy of the prisoner's dilemma under the condition of maximum entanglement is studied in detail under the condition of a collective-dephasing noise channel,and the following conclusions are drawn:By constructing a quantum prisoner's dilemma game model under collective-dephasing noise,analyzed the influence of noise parameters on the player payoff,found that the players' payoff function showed periodicity on noise parameters,and in a noise parameter period,when the collective-dephasing noise belongs to the specific noise subinterval,quantum prisoner's dilemma of Nash equilibrium exists three conditions: First,there is a unique Nash equilibrium,and neither of the Nash equilibrium strategies of the two players contains noise parameters.In this case,the two players can reach an agreement,but the payoffs they can get are functions of noise parameters;Second,there is no unique Nash equilibrium.The Nash equilibrium strategy of players is a function of noise parameters.When two players reach a Nash equilibrium,they can obtain Pareto optimal payoff;Third,there is no Nash equilibrium,and the two players fall into a rock-paper-scissors loop.