<p style='text-indent:20px;'>This paper investigates a manufacturer's retail outsourcing strategies under different competition modes with economies of scale. We focus on the effects market modes, scale and competitor's behavior decisions, then we develop four game models three modes. Firstly, find channel structure where both manufacturers choose cannot be an equilibrium Cournot competit...

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is shown that if the perturbed harmonic oscillator with a homogeneous cubic-polynomial potential and the perturbed harmonic oscillator with a hom...

This paper focuses on the role that production subsidies play in a Bertrand mixed duopoly. The paper examines four regimes: mixed and private duopoly, each with and without subsidies. The results of this study are compared with the findings of the existing Cournot mixed market literature. As a result, the paper shows that that the introduction of production subsidies into the analyses of Bertra...