Two-Player Continuous Game Theory for Product Portfolio Management in a Competitive Manufacturing Market

Nowadays, the variety of new products will run serious competitions among manufacturers. Product Portfolio Management (PPM) as an appropriate tool can influence the customer’s taste and increase the profit of firms. In this paper, the factors of PPM, production planning, and a two-player continuous game theory are considered simultaneously. Some constraints are also assumed including the availability of raw materials and demand of each product based on some specific criteria. Two firms have offered same products and competed with each other. The relationships between two producers are modeled by a non-zero two- player game. A numerical example is also presented. The proposed model is run within a single period with the inventory equal to zero at the beginning and end of this period. The objective functions show the profit of products and the constraints represent the utility of products for each customer, market's share as a function of the probability of customer selection for each section, type of distribution function for sale quantity, accessible quantity of the sum of used materials by two producers, etc. The results showed a change in demand would affect the profit of two players and the second player would be more vulnerable to this effect than the first one. In addition, a change in the sale price affects the profit of two players and the first player is more influenced by this change than the first one. The obtained data showed that with an increase in the extra sale price, the profit of the first player would increase while the profit of second player would remain approximately constant.