多再制造商回收定价竞争博弈

多个再制造商在同一回收市场中获取废旧产品并进行再制造,他们之间存在回收竞争.每个再制造商回收废旧产品的数量取决于自身付出的回收价格,同时和对手们的回收价格相关.目标是最大化各自的期望利润.本文首先利用优化理论和非合作博弈理论,证明了该博弈作为超模博弈,存在唯一的Nash均衡.然后通过比较发现竞争下的Nash均衡价格高于串谋下的合作均衡价格.最后通过数值仿真探讨了再制造商的数目和再制造成本对博弈的影响.

A Non-cooperative Game on the Acquisition Pricing of Multiple Remanufacturers

Remanufacturing is an environmentally and economically sound way to process used products because it poses great opportunities for saving resources,improving productivity and reducing manufacturing costs.To realize these opportunities,acquiring the used product is regarded as the first step in the remanufacturing process.One widely adopted approach to collect used products is to utilize a market-driven channel by paying an acquisition price to end-users.This approach can help reduce the number of used products for remanufacturing.Moreover,the competition in the used product acquisition has been a prevailing phenomenon,especially when a number of remanufacturers produce same products and collect the used ones from end-users inthe same region. These remanufacturers utilize the acquisition price as a competitive strategy to compete with others and voluntarily increase the acquisition quantity.This paper considers that multiple remanufacturers acquire used products and compete in the acquisition price.The acquisition quantity of each remanufacturer is a deterministic function of not only its acquisition price,but also the acquisition price offered by its competitors.Also,each remanufacturer faces infinite sales market for remanufactured products,and determines the acquisition price to maximize profit.We establish a non-cooperative game model on help determine the acquisition price for multiple remanufactures by using generalized acquisition functions,and utilize optimization and game theories to analyze and solve the pricing issue.First,we solve the acquisition price decision problem for each remanufacturer with information about the competitor’s pricing vector,and prove this acquisition pricing game is a super modular game.Then,we analyze the remanufacturer’s objective function Hessian Matrix,and prove that this game has a unique Nash equilibrium.In addition,we explore the cooperative equilibrium and compare it with the Nash equilibrium.The study shows that acquisition competition will encourage remanufactures to raise the acquisition price so that the acquisition quantity of used products can be increased.Finally,numerical examples are provided to show more managerial insights on the number of participating remanufacturers and the remanufacturing cost.In addition,when there are more remanufacturers in the collection market,the Nash equilibrium acquisition price will increase and the cooperative equilibrium acquisition price will decrease.This finding affirms the necessity of cooperation among remanufacturers.Furthermore,although a remanufacturer’s pricing decision and profit are highly related to its own remanufacturing cost,these decisions are insensitive to competitors’ cost. In sum,acquisition competition has been a common phenomenon in the remanufacturing industry.This paper establishes an acquisition pricing game model and proves that this game has a unique Nash equilibrium under generalized acquisition functions.In addition,this study not only finds that the acquisition price in Nash equilibrium is higher than the price in cooperative equilibrium,but also provides insights on the number of remanufacturers and the remanufacturing cost.