Inventory competition in a multi channel distribution system: The Nash and Stackelberg game

This paper investigates inventory management in a multi channel distribution system consisting of a manufacturer, with a single product, and an arbitrary number of retailers that face stochastic demand. Existence of the pure Nash equilibrium is proved and parameter restriction, which implies its uniqueness, is derived. Also, the Stackelberg game, where the manufacturer plays the role of leader is discussed. Under specified parameter restrictions which guarantee profitability, a sufficient condition for the uniqueness of the Stackelberg equilibrium is obtained. In addition, a comparison with a simultaneous move game is made. The results show that when whole prices are equal to production cost, the manufacturer carries more inventory than in the simultaneous move game.