Research On Nash Equilibrium Solution Of Quantum Prisoner's Dilemma Model Under Phase And Amplitude Damped Channels

Quantum game theory is an interdisciplinary study of game theory using quantum information theory as a tool.The expansion of the corresponding classic game strategy set and the introduction of entanglement can largely solve some problems that cannot be solved in classic games.The Prisoner's Dilemma has attracted much attention as an important model in classic game theory.This example lays the theoretical foundation for non-cooperative game theory and is widely used in real life.Based on this,in view of the decoherence phenomenon that the external environment in the open quantum system affects the system itself,this article uses quantum game related theories,establishes a quantum prisoner's dilemma game model through the EWL quantization scheme,discusses and analyzes and obtains the participants' income Equilibrium solution with Nash provides a certain reference for decision-making to propose a feasible solution to the prisoner's dilemma under the open quantum system.The main contents of this article are as follows.Using the EWL quantum scheme,based on the classic prisoner's dilemma model,the quantum game model under the two conditions of amplitude damping channel and phase damping channel is established.In the three cases of no memory,complete memory and conditional memory,the participants' income and Nash equilibrium solution were obtained in the model,and the effects of noise intensity and memory parameters on the Nash equilibrium solution were analyzed,the results show that:(1)Under the condition of phase damping channel,when the noise intensity without memory is less than the threshold of 0.3852,the noise has no effect on Nash equilibrium;however,the intensity of noise during complete memory will not affect the Nash equilibrium solution.This shows that the phase damping channel is very stable under complete memory conditions.In the case of conditional memory,the noise intensity and memory parameters together affect the Nash equilibrium solution.(2)Under the condition of amplitude damping channel,when the noise intensity whithout memory is less than the threshold of 0.8764,the noise has no effect on the Nash equilibrium;while the threshold increases to 0.9654 when the memory is complete.This shows that the amplitude damping channel tends to be more stable under complete memory than without memory,and is not easily affected by the external environment.Similary,in the case of conditional memory,the noise intensity and memory parameters together affect the Nash equilibrium solution.