Study of Decoherence in Quantum Cournot Duopoly Game Using Modified EWL Scheme

The newly proposed modified Eisert-Wilkens-Lewenstein scheme can be widely used to understand any quantum game through quantum operators. This scheme provides a vast range of two-qubit entangling operators which is otherwise not possible using the traditional Eisert-Wilkens-Lewenstein scheme (EWL) and the Marinatto-Weber scheme (MW). In our work, the proposed modified EWL scheme is further explored in noisy market games. Decoherence commonly known as noise is an unavoidable interaction of the system with the surroundings. We analyze the effects of decoherence in the Cournot duopoly game when amplitude damping is present in either of the communication channels. We find an interesting result that decoherence affects channel 2 but does not affect channel 1. Furthermore, we discover that the effect of decoherence can be partially mitigated by selecting an appropriate entangling operator.