A GAME THEORETIC APPROACH FOR PRICING OF TWO SUBSTITUTE PRODUCTS WITH SPECIFIED PRICE OF ONE MAIN COMPLEMENTARY PRODUCT

Today's business has rapidly changed and has become more competitive. In today's world, existing the competitors is an undeniable rule; therefore, for any manufacturer, appropriate decision making requires taking into account the competitors and their policy decisions. In today's competitive market, pricing is one of the important decisions for the success of a company. So, assessing the impacts of pricing strategies on demand and prot is very important. On the other hand, product pricing is one of the most important decisions and a strategic problem for manufacturers that is aected by pricing decisions made by the other producers. In the non-cooperative games, each member is a separate economic entity that makes its operational decisions independently. The Nash game is an equal power game. In this paper, for the rst time, the pricing problem for two substitute products in the present of one main complementary product is studied and Nash equilibrium prices have been introduced as well as demand and prot functions. After comparing the equilibrium prices, demand and prots, the eects of some important parameters on prices, demand and prot are addressed. The results show that the equilibrium prices of the complements products could be less or greater than the main complementary product price in comparison with each other. The threshold of this change has been provided. The parametric analysis shows that the increasing of the main complementary product price increases the related manufacturer prot with decreasing rate and ultimately reduce the own manufacturer prot. The threshold of this change is, also, calculated. Finally, a numerical example is presented and the results discussed. The numerical example veried the analytical results. This research can be expanded from some aspect such as 1) Considering a supply chain with three manufacturers and retailers. 2) Considering dynamic pricing and using dierential game theory for solving and addressing it. 3) Considering other decisions such as inventory and lot sizing to it.