On the justification of applying quantum strategies to the Prisoners' Dilemma and mechanism design

The Prisoners' Dilemma is perhaps the most famous model in the field of game theory. Consequently, it is natural to investigate its quantum version when one considers to apply quantum strategies to game theory. There are two main results in this paper: 1) The well-known Prisoners' Dilemma can be categorized into three types and only the third type is adaptable for quantum strategies. 2) As a reverse problem of game theory, mechanism design provides a better circumstance for quantum strategies than game theory does.