Abstract: Yield uncertainty is an important problem in today's competitive market. In many industries such as the cell phone and the equipment manufacturing industry, random yield has large impact on production process of component suppliers or original equipment manufacturers. Therefore, yield uncertainty will results in a random shortage of manufacturer's actual output and the loss of its regular customers. Customers who prefer to buy some product may switch to buy another substitute, if they find what they prefer unavailable on the shelf. So, inventory competition under yield uncertainty is very important problem faced by firms.The multi-period duopoly inventory games problem under yield uncertainty is addressed in this paper. Two firms sell two substitutable products in multi-periods, respectively, and some unsatisfied customers will switch to buy another productif one of them is out of store. In each period, they are competing for substitute demand by make their order decisions. The existence of the Nash equilibrium is proved, its structure is characterized and the impact of the yield uncertainty and substitution rate on the Nash Equilibrium is discussed. It is found that yield uncertainty results in multiplicity of Nash equilibrium. We give conditions under which the equilibrium is unique are given. Furthermore, we show that the equilibrium order quantity is increasing in the substitution rate, and the firm with lower yield uncertainty can earn more profit.Numerical experiments are conducted to study the impact of the substation rate and supply reliability on the firms' order quantities and profits.

Key words: random yield, inventorygame, Nash Equilibrium, inventory management