Quantum Games With Restrictions

Game theory is widely used in social science and biology. It is one of the foundations of modern economy. In physical view, the procedure of a game is a process of information in-deed. We know that microscopic physics is described by quantum theory. When the medium is a microscopic system, the information is quantum information. So game theory and quantum theory form a new subject - quantum game theory, which has displayed a wide prospect of application. A lot of quantum information procedure can be regarded as quantum game. So the research of quantum game is helpful for quantum algorithm and quantum communication.The thesis consists of five chapters. In chapter one we briefly recall the basic theory of the game and quantum game, then we introduce some significant works of this aspect.In chapter two, we study the influence of the constraint in the parameter space on quantum games. Having decomposed SU(2) operator into product of three rotation operators and controlled one kind of them, we impose a constraint on the parameter space of the players' operator. We find that the constraint could provide a tuner to make the bilateral payoffs equal, so that the mismatch of the players' action at multi-equilibrium could be avoided. We also find that the game exhibited an intriguing structure as a function of the parameter of the controlled operators, which is useful for making game models.In chapter three, we study the quantum games where the players have different strategic spaces (The restrictions to players' strategic spaces are different). We restrict Bob to classical strategic space and Alice to different quantum pure strategic spaces. We find that the player who can use a quantum strategic space does not always possess more payoffs than the player who is restricted to apply only classical strategies. We find the condition of the classical player getting more payoffs than the quantum player. We also find the game exhibit intriguing structures.In chapter four, we present a linear optical proposal for implementing the quantum games. We also give an universal scheme for implementing the games by using any quantum computer.In chapter five a summary of the work and an outlook of this aspect aregiven.