The Complexity Of Quantum Game Dynamic Systems With Heterogeneous Players

Quantum games have advantages over classical games,and provide new ways for us to solve many problems in games.The quantization of classical games offers the possibility of achieving Pareto optimality due to the existence of quantum entanglement.Combining quantum game theory with nonlinear dynamics can not only solve the difficulties in classical games,but also analyze the stability conditions of quantum Nash equilibria,and explore the complex behaviors of nonlinear dynamic systems under bounded rational expectations.The tragedy of the commons is an economic problem in the real world,and how to get rid of the ”tragedy” has always been a focus of scholars.The Cournot oligopoly game with asymmetrical information can reflect the situation of information imbalance and incomplete in the real economy,Bayes-Nash equilibria are also a current research hotspot.Combining quantum game and nonlinear dynamic theory,this thesis constructs two quantum dynamic systems.The main contents and conclusions of this thesis are as follows:This thesis first builds a nonlinear dynamic system of the Commons’ tragedy with quantum strategies and heterogeneous players in discrete time.Then,we obtain a sufficient and necessary condition for quantum Nash equilibria to be stable equilibria.Finally,the impacts of quantum entanglement on the stable region of systems are investigated,and the behaviors of complex dynamical systems are analyzed.The results show that quantum Nash equilibria are stable points of nonlinear dynamics for quantum Commons’ tragedy if both quantum entanglement and quantum strategy adjustment speed satisfy certain conditions.In addition,numerical simulations discuss the features of nonlinear dynamics,the numerical results show that nonlinear dynamics appear chaotic if the adjustment speed of quantum strategy is larger or the quantum entanglement degree is smaller.the dynamics of a quantum Cournot duopoly with asymmetric information and heterogeneous players in discrete time is established by combining the quantum games and chaotic dynamics theory.Theoretical results on the local stability of the quantum Bayes-Nash equilibria are obtained by analysis.In addition,the nonlinear dynamical behaviors are discussed by numerical simulations,the results indicate that market failure due to high costs can be regulated by appropriately adjusting the degree of quantum entanglement.