We present models for competition among multiple suppliers for demand from a single manufacturer. The suppliers produce to stock a single product and are allocated demand by the manufacturer based on the amount the amount of inventory they hold. We prove the existence of a Nash equilibrium for a broad class of market allocation schemes. For the special case of identical suppliers under either a stock-proportional or fill rate-proportional allocation, we show the uniqueness of the Nash equilibrium. Analysis of the Nash equilibrium for this case reveals that (a) the manufacturer benefits from competition (in the form of higher fill rates), (b) the manufacturer benefits more from a stock-proportional allocation than a fill rate-proportional allocation, and (c) the manufacturer benefits the most when the number of suppliers is two.
Ehsan Elahi, Saif Benjaafar, and Karen Donohue. "INVENTORY COMPETITION IN MAKE-TO-STOCK SYSTEMS" Proceedings of the Fourth Aegean Conference on Analysis of Manufacturing Systems, Samos, Greece (2003). http://scholarworks.umb.edu/msis_faculty_pubs/5