Quantum Cournot Triopoly Game with Heterogeneous Expectations: Dynamics and Chaos Control with Isoelastic Demand

This paper investigates how quantum entanglement and heterogeneous expectations jointly affect the stability, complexity, and controllability of a Cournot triopoly with isoelastic demand. Based on the Li–Du–Massar quantization scheme, we construct a discrete-time quantum Cournot triopoly in which three firms adopt different updating mechanisms: boundedly rational adjustment, naïve and adaptive expectations. The quantum boundary equilibrium and the unique interior quantum Nash equilibrium are derived explicitly. By linearizing the resulting three-dimensional nonlinear map and applying the Jury criterion, we obtain analytical local stability conditions for the interior equilibrium. The results show that increasing the entanglement level reduces the admissible range of the adjustment speed, thereby shrinking the stability domain and making the market dynamics more prone to bifurcation and chaos. Numerical simulations further reveal a typical transition from stable convergence to flip bifurcation, period-doubling cascades, chaotic attractors, and sensitive dependence on initial conditions. Finally, a control parameter is introduced to rescale the effective adjustment speed of the boundedly rational firm. This mechanism preserves the equilibrium set while restoring convergence to a stable fixed point once the control intensity exceeds a critical threshold. The findings highlight the joint role of entanglement, expectation heterogeneity, and nonlinear demand in shaping complex quantum oligopoly dynamics.