Abstract 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 , difference in marginal costs ( k ) and elasticity of demand on the optimal profits of both firms. The results show that the existence region decreases with γ and k increasing. A larger elasticity of demand can destroy the profits of both firms. If positive γ and k are more favourable to the profits of two firms. If the first firm's profit increases with γ increasing for fixed k , but decreases with k increasing for fixed γ . The second firm's profit increases with k increasing for any fixed γ . As to the influences of γ on the second firm's profit, when k is less than a critical value, it increases with γ increasing, otherwise it decreases with γ increasing for fixed k .

Stackelberg's duopoly. In this model, the firms move sequentially to determine their quantities (see Stackelberg competition). Cournot's duopoly. In this model An oligopoly (from Ancient Greek ὀλίγος (olígos) 'few' and πωλέω (pōléō) 'to sell') is a market in which pricing control lies in the hands of a few sellers. As a result of their significant market power, firms in oligopolistic markets can influence prices through manipulating the supply function. Firms in an oligopoly are mutually interdependent, as any action by one firm is expected to affect o Q 2 = 2 ( M − C M ) − 2 Q 1 = 96 − 2 Q 1 {\displaystyle Q_{2}=2(M-C_{M})-2Q_{1}=96-2Q_{1}} [1.2] Equation 1.1 is the reaction function for firm 1 {\displaystyle 1} . Equation 1.2 is the reaction function for firm 2 {\displaystyle 2} . The Nash equilibrium can thus be obtained by solving the equations simultaneously or graphically. Reaction functions are not necessarily symmetric. Firms may face differing cost functions, in which case the reaction functions and equilibrium quantities would not be identical.