Quantum prisoner’s dilemma in a restricted one-parameter strategic space

摘要

Choosing a suitable restricted strategic space is crucial for the novel features of quantum games. Based on the Eisert–Wilkens–Lewenstein quantization scheme, a quantum prisoner’s dilemma is introduced using a simple restricted one-parameter strategic space. Our scheme is found to preserve the quantum advantages of the Eisert–Wilkens–Lewenstein scheme, and improve its Nash equilibrium characteristics. The simplicity of the calculations enables us to address some important aspects of quantum games which can be applied to many real systems. The robustness of Nash equilibria to corruption in the initial state is studied, and a measure of robustness is defined. The robustness of Nash equilibria is found to scale inversely with the entanglement. Our scheme is applied to various prisoner’s dilemma games having different dilemma strength. Also, Some variant forms of restricted one-parameter strategic space are studied.