顾客退货影响的零售商定价和库存博弈模型

A pricing and inventory game model of competitive retailers with customer returns

研究了具有顾客退货影响的竞争性零售商的定价和库存决策.考虑存在与定价和库存成线性关系的退货量函数,建立了同时具有价格和库存竞争的零售商非合作博弈模型,验证了零售商的期望利润函数为关于价格和安全库存的拟凹函数,证明了纯战略纳什均衡的存在性.利用压缩映射定理给出了纯战略纳什均衡唯一存在的充分条件.提出了博弈存在唯一的对称性纯战略纳什均衡解,分析了该纳什均衡解对于退货系数的比较静态性质,并总结了顾客退货对于定价、库存及期望利润的影响.研究表明,顾客退货对于定价和库存影响表现出一定的不确定性;退货一定会引起零售商期望利润的降低,但价格和库存竞争强度的增大有益于弱化顾客退货的影响.

This paper analyzes two competitive retailers＇ pricing and inventory decision-making problem con- sidering the impact of customer returns. Considering a return function which has linear relationship with price and inventory, it establishes a non-cooperative game theory model of two retailers under simultaneous price and inventory competition. It verifies the retailer＇s expected profit is a joint quasi-concave function of price and safety stock, thus the existence of the pure-strategy Nash equilibrium is proved. Moreover, it provides a suffi- cient condition for the pure-strategy Nash equilibrium to be unique by the fixed point theorem of contraction mapping. Then, this paper analyzes the comparative static results of the returns coefficient to the pure-strategy Nash equilibrium under the symmetric case. Furthermore, it summarizes the effect of customer returns on the retailer＇s pricing, inventory and expected profits. The results show that the impact of customer returns on the retailer＇s pricing and inventory is uncertain; The existing returns can decrease the expected profits. However, strong competition will be beneficial to mitigate the customer returns＇ impact.