Nash Equilibrium Analysis Of The Chicken Game Model Based On Two Different Quantum Schemes

As an emerging discipline,the quantum game theory gives superiority to the classic game theory.Since the case of the chicken game can be seen frequently in real life,it is of great practical significance to study the chicken game model.In the classic chicken game model,one chooses cooperation and the other chooses not-cooperation is the Nash equilibrium solution of the game model,however both sides choose to cooperate with each other consistently is the pareto optimal solution of the game,so the classic chicken game model exists cooperation dilemma.Therefore,this paper applied a relevant theory of quantum game theory to the classic chicken game model,which was then established with an EWL quantum scheme and an MW quantum scheme respectively.Based on the analysis of the equilibrium of the strategic combination,the Nash equilibrium solution of the model was derived,providing a solution to the dilemma in the classic chicken game and realizing the successful transformation of the chicken game from non-cooperation to cooperation.The main content of this article:(1)From the perspective of entangled state,by using EWL quantum scheme and taking the parameters of the strategy space as variables The strategy combination of the quantum chicken game can be obtained when strategy space is one parameter or two parameters,.By analyzing the equilibrium of the strategic combination in each different cases,the corresponding Nash equilibrium solution of the game model is can be obtained.Also,the influence of the entanglement on the Nash equilibrium solution was discussed,and the Nash equilibrium solution was numerically simulated to eventually present the Nash equilibrium solution distribution map,providing new thoughts for the transformation of the chicken game from non-cooperation to cooperation.(2)From the perspective of the superposition state,and by using the MW quantum scheme,this thesis is based on the initial state |?in>=a|CC>+b|CD>+c|DC>+d|DD>of the general quantum chicken game.The Nash equilibrium solution of the quantum chicken game was demonstrated,and the influence of the initial state coefficient on the Nash equilibrium solution was discussed to ultimately present a solution to the dilemma of the classic chicken game.