The Quantization Analysis Of Cournot Game Model And Generalization

Quantum game is a new subject in the last 20 years which use quantum information theory as a tool to study game theory.It is better than the classic game,reflecting in the work that the quantum game expand strategy set greatly,the introduction of entanglement give a effective solution to the difficulties in classical game theory.It has been widely infiltrated into economics,information science,biology and other related fields.Cournot model is one of the famous classic model in game theory in which the phenomenon of the prisoner's dilemma has not been resolved.In the paper,it uses the knowledge of quantum game theory,the classical Cournot game model is quantized by the scheme proposed by Marinatto and Weber,and then generalized to the case of multiplayer.It establishes the multiplayer quantum game model and calculates the equilibrium solution and the profit,then analyzes the conflict of interest in the case of multiplayer Cournot model,and resolved the contradiction between individual interest and collective interest.The paper is divided into four chapters.The first chapter analyzes the background of the paper,significance,research status,the used tools and innovations.The second chapter is the study of Cournot Game Model under Marinatto-Weber quantum scheme.The third chapter is the study of multiplayer Cournot quantum game model.The fourth chapter is the conclusions and prospects.The main research work is as follows:(1)Using the knowledge of quantum game theory,it establishes Cournot quantum game model under different initial state by the Marinatto-Weber scheme,then calculates the equilibrium solution and equilibrium profit and compares with the classic game,it points out the superioty of quantum game model and uses numerical simulation to verify conclusions.(2)Using the knowledge of quantum game theory,it establishes multiplayer Cournot quantum game model by the Eisert quantum scheme,then calculates the equilibrium solution and the profit and analyzes the influence of entanglement on them.