Competing dynamics: Analyzing market share in a duopoly

One of the main measures of success in business is a company’s market share, and understanding the cause and effect of various economic factors on market share is very important in the success of a company. In this paper we study market shares between two manufacturers in a duopoly economy. An optimal pricing strategy for a company to achieve the most market share in a duopoly economy is proposed. Two numerical models, based on ordinary differential equations, for the market share are developed to study the company’s success in the market. One model considers the quantity demand and investment in research and development, while the other model focuses on a more realistic relationship between the quantity demand and the price.