Asymmetric Quantum Stackelberg Duopoly Game Based on Isoelastic Demand

A quantum Stackelberg duopoly with isoelastic demand is proposed by using Qin et al.’s asymmetric quantization scheme. The existed conditions of quantum equilibrium are investigated, constituted by three parameters: the relative marginal cost m, and two different entanglement factors γ and α. On this basis, the impacts of γ and α on the leader’s and the follower’s optimal profits u1∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {u}_1^{\ast } $$\end{document} and u2∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {u}_2^{\ast } $$\end{document}, the first-mover advantage δu∗ and the total product quantity Q∗ are analyzed. A positive γ will increase u1∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {u}_1^{\ast } $$\end{document} and u2∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {u}_2^{\ast } $$\end{document}, reduce Q∗, and, depending on m, increase or reduce δu∗. Nevertheless, the influences of α are exactly the opposite. The results of the asymmetric Stackelberg duopoly with isoelastic demand are different from the case with linear demand. To better manage the market, one should consider the market structure besides choose proper entanglement factors.