Quantum Strategies In Moving Frames

Quantum game theory is on the case in which the players make use of some carriers which have quantum properties(such as particles) and adopt quantum operations as strategies.Researches show that quantum strategies could make the players gain better payoffs and equilibria than classical strategies.For example,as for classical "Prisoner's Dilemma",quantum strategies would help the players escape from the classical dilemma,and have a new equilibrium,thus,the players can have better payoffs.From this point of view,Quantum Game worths further research.An elementary particle has quantum properties,as well as relativistic ones.When a particle moves at very high speed,an observer in a static frame would find that some properties of the particle(such as the direction of spin) change;when two entangled particles move at very high speed,the observer may find the degree of entanglement of the two particles changes.These changes on quantum properties may have significant impact on the game,thus,they may change the game and give birth to some new equilibria.We investigate quantum strategies in moving frames by considering Prisoner's Dilemma and propose fbur thresholds ofγfor two players to determine their Nash Equilibria.We find that the relativistic operations could enhance or diminish the quantum features of the game for different players who move in different directions relative to the arbiter.The structure of this article is set as follows:ChapterⅠintroduces some aspects of Classical Game Theory,such as the history, important theorems,propositions,notation rules,and so on.This part is the fbunda-tion of this article,as well as the jumping-off point. ChapterⅡintroduces the researching development of Quantum Game Theory, as well as some common methods,especially fbr the research on Quantum Prisoner's Dilemma,because it is the theoretical model in this article.ChapterⅢintroduces the properties of the spin state of single particle and quantum entanglement under Lorentz transfbrmation,which is the theoretical basis to extend Quantum Prisoner's Dilemma into relativistic case.ChapterⅣparticularly addresses some of my work on Relativistic Quantum Game Theory,demonstrating some interesting phenomena which worth further research.The main original point of this article is to extend the existing model of quantum game—Quantum Prisoner's Dilemma to a relativistic and quantum case,and to analyze the new strategy equilibria which may appear in this situation,thus,to explore the influence that the relativistic effect may cause on quantum games.The research on relativistic quantum games can not only help us understand the physical essences of Game Theory,but also guide remote games and the games between different frames.For instance,in a remote game,players should emit their particles(at high speed) to the arbiter,and this behavior may change the spins and entanglement of the particles,which may have influence on the result of the game. This influence is just what the Relativistic Quantum Game Theory should research.