Quantum Cournot duopoly game with general isoelastic demand and asymmetric production costs

This letter explores the quantum version of a Cournot duopoly game with general isoelastic demand and asymmetric production costs by applying Li-Du-Massar's minimal quantization rules, and it especially analyzes the existence region of quantum equilibrium, and the influences of quantum entanglement (gamma), difference in marginal costs (k) and elasticity of demand (eta) on the optimal profits of both firms. The results show that the existence region decreases with gamma and k increasing. A larger elasticity of demand can destroy the profits of both firms. If 0 < eta < 1, positive gamma and k are more favourable to the profits of two firms. If eta >= 1, the first firm's profit increases with gamma increasing for fixed k, but decreases with k increasing for fixed gamma. The second firm's profit increases with k increasing for any fixed gamma. As to the influences of gamma on the second firm's profit, when k is less than a critical value, it increases with gamma increasing, otherwise it decreases with gamma increasing for fixed k. Copyright (C) 2022 EPLA