Theoretical Study On Quantum Games

In recent years,quantum game theory as a theoretical frontier of the game theory,has attracted a great deal of attention.The reason to investigate games quantum mechanically is that we can extend the game strategy space by using superpo,sition,entanglement,and interference in quantum mechanics,and obtain the results of those we cannot obtain in the classic game.In this thesis,we mainly consider some quantum static and dynamic games and aim to study the advantage of the quantum game.Firstly,one type of quantum static games is investigated.We consider a four-company-price game.It is found that the Nash Equilibrium(NE)of the classical game is a "prisoner's dilemma".We quantize the classical game and get the quantum game model 1.We dis-cuss the effect of entanglement on Nash Equilibrium of model 1 and find there is a critical value of entanglement.When the entanglement is less than the critical value,model I is the same as that of classical game.Otherwise,the quantum game is better than the classical game,the four companies can perfectly escape the dilemma.Furthermore,the quantum game model 2 of the relation between single company payoff and decoherence is established.In terms of firm payoff,model 2 is less than the model 1,but larger than the classical game.Secondly,a dynamic quantum game-a repeated game is discussed.We generalize P.Frackiewicz's(PF)method,and study a twice-repeated pricing game in the quantum domain.Two firms play this game,and both firms have three pricing strategies.By establishing the quantum model of the twice-repeated pricing game,we get three pure-strategy Nash equilibriums in every stage of the game,and equilibrium payoff of both firms.Comparing the result of quantum twice-repeated pricing game with that of classical one,the advantage of quantum game will be demonstrated.Lastly,we conclude our work and indicate the future work and potential research trend.