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

This paper investigates inventory management in a multi channel distribution system consistingof 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. underspecified parameter restrictions which guarantee profitability, a sufficient condition for the uniqueness ofthe stackelberg equilibrium is obtained. in addition, a comparison with a simultaneous move game ismade. the results show that when whole prices are equal to production cost, the manufacturer carriesmore inventory than in the simultaneous move game.