  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.
