Research On Multi-player Quantum Game Protocols Based On Nash-equilibrium

Quantum game as an important part of game theory extends game theory from classical world to quantum world.Quantum game can solve some problems that cannot be solved by using classical resources.Nash-equilibrium plays a very important role in game theory.There are lots of games based on Nash-equilibrium by using classical resources.The purpose of the thesis is to study the ability of quantum resources to surpass classical resources in game theory.For exploring the quantum advantage,this thesis proposes one three-player dynamic zero-sum game protocol with complete and perfect information.Firstly,with two different settings,it shows that there is no three-player fair zero-sum game using classical resources without the arbitration.And then,after the quantizing classical settings,two new games will be constructed using quantum superposition states.Both are asymptotically fair,that is,the quantum games can achieve absolute fairness when the free parameter tends to infinity.In addition,quantum games have dynamic adaptability,that is,the average payment of players can change dynamically with respect to the initial information.Finally,it shows that the quantum games are robust to measurement error and system noise.One multi-player dynamic zero-sum game protocol is then built with complete but imperfect information.Under certain conditions,it shows that the classical resources can not be used to realize the multi-player fair game without the arbitration.It is different for quantum scenarios.After quantizing the classical settings,the quantum game protocol will be constructed using entangled state resources.This scheme can achieve fairness.In addition,quantum game has dynamic adaptability,that is,the average return of some participants can change dynamically with the initial information.Moreover,the initial information can change dynamically with the free parameters.Finally,it shows that the quantum game is robust to measurement error and system noise.