Application of Game Theory on Inventory Level Decision Making

Abstract

Many companies producing durable products, profit more from spares than the base parts. In a competitive and uncertain aftermarket, an Original Equipment Manufacturer (OEM) can benefit from Game Theory to manage spare parts inventories. We study the spare parts inventory game as an N-person non-zero-sum single-shot game where players play simultaneously. The game is restricted to a two-player (the OEM and the market) non-cooperative game setup. The market is an unreasoning entity whose strategic choices affect the payoff of the OEM, with no interest in the outcome of the game. This is a game against nature, which means the OEM plays against the market. The OEM decides on a pricing strategy (in a competitive manner with low cost manufacturers or will-fitters to absorb more customers) and the order-up-to stock level, and its inventory level strategy is not dominated – i.e. the game has a mixed strategy solution. This solution maximizes the payoff for the OEM by setting the price and the inventory level based on assumptions on the lower and upper bounds of the demand’s distribution parameters.