Research On Some Issues Of Multi-Player Quantum Game

Quantum game theory is the combination of classical game theory and quantum mechanics. Through David A. Meyer’s paper of quantum PQ penny flipover, we know the advantage of quantum game. Quantum game theory has already developed into an independent discipline and has wide applicability in all aspects of our lives. In fact, many processes can be regarded as competition games. The games are not only related to two-player games, but also concern multi-player games.The paper describes and analyzes the multi-player quantum game on two aspects:the best result of the game and the coalition of multi-player non-cooperative game. Main contributions of this paper are as follows:For multi-player non-cooperative game, our study mainly focuses on minority game. First, we calculate and prove the minimum and the upper limite of the expected payoff. Second, we design control-target scheme and use it to design the processes of multi-player two-choice minority game and multi-player multi-choice minority game. All of them had the best results. Thirdly, we consider the quantum coalition of multi-player minority game and find the one of the best coalition strategy ("n equipartition" compound mode). Fourth, we analyze the relationship between coalition and initial state. This result provides a theory basis for the choice of the initial state in a minority game and we get that some players can always improve their expected payoff through coalition sometimes. For multi-player cooperative game, our study mainly focuses on pure coordination game. We extend it to multi-player multi-choice pure coordination game. The paper use the control-target scheme to design the process of pure coordination game and make it has unique equilibrium. We use class-control-target scheme to design the process of the multi-player multi-choice pure coordination game and make it have the best result.