基于Bertrand闭环供应链的企业价格博弈模型

设计了一个具有供应商和两个零售商组成的Bertrand双寡头价格博弈的主从闭环供应链系统，给出了分散和集中两种模式下批发价、零售价、回收价以及各方利润的具体表达式并进行了比较，研究了供应链整体利润与产品和废弃品替代率的关系。最后，在此基础上分析了分散模式下零售商和生产商的具体对策，提出了两阶段数量折扣协调策略实现帕累托改进，并求出了折扣率和补贴率的具体范围，为进一步研究更一般的闭环供应链系统打下理论基础。

A Game Model for Pricing in Bertrand Closed-loop Supply Chain Systems

The operation of reverse supply chain is discussed in this paper. Based on the Bertrand duopoly pricing game, a game model is developed for a closed loop supply chain composed of a supplier and two oligopoly retailers. With this model, the pricing mechanism for wholesale, retail, and recycling is analyzed under both centralized and decentralized decision making modes. Also, by using the model, the relationship between the supply chain profit and the product replacement rate is investigated. Based on the analysis, a two stage quantity discount policy in pricing is proposed such that the performance is improved in the sense of Pareto optimization. The range of discount and subsidy rates is given for both centralized and decentralized modes. The results obtained provide the basis for establishing the theory of closed loop supply chain system.