Study On The Evolutionary Stability Of Stag Hunt Quantum Game Model Under The Different Conditions

Evolutionary game theory and quantum game theory,as the two important branches of game theory research,have been widely applied in physics,economics,biology and other fields.At present,evolutionary game theory and quantum game theory are getting more and more attention from academia.In nature,the phenomenon of competition and cooperation can be seen everywhere.Whether in the field of biology,predators choose to act alone or collectively,or in the field of economics,enterprises choose to compete or cooperate to achieve win-win situation.These are all practical problems that need to be solved urgently and stag hunt game can explain the hidden rule of these practical problems.In order to study the related problems of stag hunt game,this paper uses the knowledge of evolutionary game and quantum game and based on the factorization method and the density matrix method to obtain the Nash equilibrium solution of quantum model,and analyzes the evolutionary stability of equilibrium solution,and finds out the factors influencing equilibrium solution,so as to provide some enlightenment for the application of stag hunt game model in practice.The main contents of this paper are as follows:(1)Based on evolutionary game theory and quantum game theory,a stag hunt quantum game model is established by using factorization method.At the same time,the profit of the quantum model and the equilibrium solution are obtained.From the perspective of evolutionary game theory,the evolutionarily stable strategy and the replicator dynamics are analyzed,and the evolutionary phase diagram is given which provide a new explanation for the dilemma in stag hunt game.(2)The quantum model of stag hunt game under different initial conditions is established by density matrix method,i.e.the initial strategy of factorization is extended.At the same time,the equilibrium solution of the quantum stag hunt game is calculated and its evolutionary stability is analyzed.The influence of different initial states and entanglement on the equilibrium solution and profit of game model are explored.And the profit function corresponding to the equilibrium solution is analyzed by numerical simulation.Finally,the conditions for stag hunt game to get rid of the "dilemma" is given.