Research On Characteristic Function Of Production Competition Under Quantum Strategy And Quantum Entanglement

Game theory is widely applied in real society as a branch of Economics in recent year?The Nobel prize in economics has been awarded to game theorists which arose more studies in this area.Quantum game is a new research method to study the game behavior in the game which successfully solving the problems such as "prisoner's dilemma","oligopoly" through extending the policy space,introducing the properties of entanglement and superposition that arrack more attentions.We divide the development process of quantum game and sum up the quantum game model involved based on the characteristics of the development of Quantum Games,and related issues in the game,then summarize the advantages of quantum game.We consider the quantum game theory focuses on the non-cooperative game and cooperative game problem,to study less,and the characteristic function is described and alliance strategies,therefore in the cooperative game selected characteristic function as the research object,in the production of a competition model of three people were using quantum strategies and classical strategies the characteristic function of the alliance,comparative analysis of properties of the characteristic function of quantum game.Then,the definition of the characteristic function is given in the form of state space description.Finally,considering the state space and density matrix can describe the state of the system,the MW model is used to describe the output competition model and the difference between the characteristic function of the Union and the classical case when the initial state is in the maximally entangled state,we present the coalition characteristic function which is under the density operator description.This paper provides a new method for describing the characteristic function in quantum cooperative games from two angles of state vector and density operator.Which is helpful to the study of the quantization of cooperative game and can be used for reference in the future.