Noisy quantum Stackelberg-Bertrand duopoly game

The Cournot model of Stackelberg duopoly is a sequential game with leader advantage. On the other hand, Bertrand model gives more advantage to follower than leader. When this follower advantage game is quantized using modified Eisert-Wilkens-Lewenstein scheme, following results are obtained: Firstly, in the noiseless case there exists a range of two qubit entangling operators which can provide leader advantage. Secondly, in the presence of noise, amplitude damping affects the follower-leader advantage more than phase damping which can be mitigated with an appropriate choice of entangling operator. Thirdly, when noise is maximum in the amplitude and phase damping channels, entangling operators do not play any role in deciding the profit function of the firms. However, entangling operators influence the game even when the noise is maximum in depolarizing channel. Hence, the quantum nature of the game is (not) killed by the maximum noise in the (depolarizing channel) amplitude and phase damping channels.