Chaos prevention in a correlated noisy dynamic Stackelberg duopoly game through the B-gate

Abstract Recent economic research has focused on applying quantum mechanical models to understand complex markets. Real markets are usually complex with nonlinear inverse demand functions and dynamic participants. Furthermore, when these market games are quantized, players interact via quantum channels that are prone to decoherence. In this work, owing to the complexity of real markets, we introduce noise and memory in a dynamic quantum Stackelberg duopoly game for the first time. We shed light on the significance of two-qubit entangling operators, particularly special perfect entanglers (SPEs), in controlling chaos. The following noteworthy observations are made: First, although entangling operators cannot prevent monopolies in the market, they can shift leader dominance to follower dominance. Second, numerical analysis highlights the significance of the B-gate in a correlated noisy channel as a chaos control. We also highlight the significance of the controlled-NOT (CNOT), and double-CNOT (DCNOT) gates in controlling chaos in noisy, memoryless channel 2. Finally, we show that the CNOT and DCNOT gates are more sensitive than the B-gate. These novel features of two-qubit entangling operators in correlated, noisy and dynamic market games shed new light on the role of SPEs in quantum dynamic game settings.