A quantum extension to inspection game

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.