  Quantum game theory is a new interdisciplinary field between game theory and
physical research. In this paper, we extend the classical inspection game into
a quantum game version by quantizing the strategy space and importing
entanglement between players. Our result shows that the quantum inspection game
has various Nash equilibrium depending on the initial quantum state of the
game. It is also shown that quantization can respectively help each player to
increase his own payoff, yet fails to bring Pareto improvement for the
collective payoff in the quantum inspection game.
