Game Theoretic Analysis of Exclusive Contract for Carbon Fiber Reinforced Plastic in the Aviation Industry

摘要

We investigate the rationality of an exclusive supply contract for Carbon Fiber Reinforced Plastic (CFRP) between one of the two largest aircraft manufacturers in the world, Boeing, and a Japanese CFRP supplier, Toray. It appears irrational that in 2004 Boeing dared to choose Toray as the sole CFRP supplier for their new B787 aircraft, and exclude other CFRP suppliers for the next 18 years, instead of letting several suppliers compete on price. On the basis of game theory, we build a mathematical model of the market for CFRP comprising Toray and the oligopolistic market for aircraft, assuming the other huge aircraft manufacturer, Airbus, as Boeing's rival. Consequently, we derive subgame perfect Nash equilibria using backward induction and observe its outcome. The results show that under specific conditions, such a contract can be a rational strategy by both companies, Boeing and Toray. In the model, an aircraft is defined as a product consisting of two materials, CFRP and aluminum. Two decision stages about production by Boeing and Airbus are done sequentially. In each stage, the amount of CFRP is first determined by the market and then the manufacturer determines the amount of aluminum. However, in advance of this stage Toray has been given a chance to propose the amount of CFRP for the case of exclusive supply. In order to be chosen as the exclusive supplier, Toray should propose the total amount of CFRP which are produced by both suppliers in the Cournot competitive market. It implies that Toray has an incentive to discount the price of CFRP from desirable price for purely monopolized market. Thus, designating a supplier as the exclusive one is rational action for manufacturers because it creates the possibility to make the price of material lower.