Cournot and Stackelberg duopoly games in the purview of modified EWL scheme

The recently proposed modified EWL scheme aims to understand the role of two-qubit entangling operators in controlling the game dynamics. In this work, we quantize the classical Cournot and Stackelberg duopoly games using the modified EWL scheme to understand duopoly games from the perspective of quantum operators. We have found two interesting results: Firstly, in both Cournot and Stackelberg duopoly, the profit function of the firms depends upon the entangling operator only when the firms adapt different strategies. Secondly, the outcome of the firms can be made equal with a suitable choice of entangling operator upon interchanging the strategies of the firms. We have shown the validity of both the theorems for pure and mixed strategies. The observation holds good for both Cournot and Stackelberg duopoly games. Further, we have shown the difference in the outcome of the firms in the Stackelberg duopoly game can be minimized to some extent with the help of suitable entangling operators and strategies.