Maple as a tool to understand marketing game for up to four companies

Abstract

In business environment, advertisement is very important. Companies spent a lot of money to advertise their products. When there are several players which have the same product to market, the competition will be quite tough since the market size is finite. The amount of the money spent for advertisement will affect the sale of the product. The profit for each company will depend on the amount of money spent for advertisement. However, this will also depend on the money spent by other companies, making the determination of the optimum profit become difficult. For two and three companies, exact value of the optimum profit for each company can be found. However, the analysis for more than three companies is quite complicated so we must resort to numerical method. Examples for the cases of two, three and four companies are given. A company with the smallest effectiveness factor and gross profit will have the smallest optimum profit. Maple has been widely used to derive formulas and to solve the case studies in this paper.