Evolutionary Quantum Cournot duopoly game in the purview of the modified EWL scheme

It is well-known that the evolutionary dynamics is widely studied in classical game settings. In this work, for the first time, the notion of evolutionary dynamics is studied in the context of quantum Cournot duopoly game using a modified EWL scheme. Unlike the well-known Eisert-Wilkens-Lewenstein scheme and the Marinatto-Weber scheme, the modified EWL scheme admits a wide range of two-qubit entangling operators which are essential to understand game theory from the perspective of quantum operators. By applying this scheme and by using replicator dynamics, it is observed that these exists only one evolutionary stable strategy (ESS). Further, the identified stable strategy plays a crucial role in replacing the strategy-profit maximization (played by majority of the population) with the mutant strategy-revenue maximization. Also, these results highlight the insignificance of the entangling operators in deciding the ESS.