在实际中，消费者购买耐用品时均同时获得厂商提供的质保服务，由于产品质保服务影响着消费者的产品使用效用，因此耐用品定价、质保期和产品质保服务投入是影响厂商利润的主要因素。考虑双寡头市场环境下，建立微分博弈模型讨论单位产品质保服务投入和产品质保期对双寡头厂商均衡价格的影响。结论表明双寡头厂商的单位产品质保服务投入越高、质保期越长，均衡价格越高；但单位产品保服务投入与质保服务对消费者效用影响系数的关系影响着竞争对手在均衡价格的变化趋势；劣势的低质量厂商可以通过增加单位产品质保服务投入策略或延长质保期的策略实现在均衡下与高质量厂商以同等价格销售耐用品，但劣势厂商增加单位产品质保服务投入策略要优于延长质保期策略。最后，利用数值分析进一步验证了所得结论的有效性。
In practice, more and more durable goods manufacturers take use of warranty service to obtian the competitive advantage. Manufacturers provide warranty service for consumers who buy durable goods. Price, warranty period and warranty service expense are the main factors influencing manufactuer's profits, due to product warranty services affecting the consumer's utility. Duopoly firms provide the same durable goods with different quality in the market.Product failure is random and subject to exponential function. Duopoly firms provide free reparation service within warranty period. In this paper' price is defined as the decision variable, and the differential game model is constructed to discuss the effect of unit product warranty service expenses and quality period on the equilibrium price for duopoly firms. And then how the inferior manufacturer achieves the same price with the high quality manufacturer through warranty period strategy is analyzed and warranty service strategy is analyzed. Results indicate that the higher the unit product warranty service expenses of duopoly firms and the longer the warranty period,the equilibrium price is higher.But the relationship between the consumer utility influence coefficient and unit product warranty service expenses affects the change of competitor's equilibrium price.The inferior manufacturer providing low quality products makes use of the strategies of increasing unit product warranty service expenses and extending warranty period to realize the same price with the high quality manufacturers under the equilibrium. In addition,the effects of different strategies of the inferior manufacturer on warranty cost are compared, and it is found out that the strategy of increasing unit product warranty service expenses is better than extending warranty period strategy. Finally, numerical analysis are used to further verify the effectiveness of the conclusion. So this paper not only provides theoretical guidance for manufacturers to implement warranty service, but also extends the scope of warranty service research.
[1] Glickman T S, Berger P D. Optimal price and protection period decisions for a product under warranty[J].Management Science, 1976, 22(12):1381-1390.
[2] Manna D K. Price warranty length decision with Glickman-Berger mode[J]. International Journal of Relibility and Safety, 2008, 2(3):221-233.
[3] Meneszes M A, Currim I S. An approach for determination of warranty length[J]. International Journal of Research in Marketing, 1992, 9(2):177-195.
[4] Douglas E J, Glennon D C, Lane J I. Warranty,quality and price in the US automobile market[J].Applied Economics, 1993, 25(1), 135-141.
[5] DeCroix G A.Optimal warranties, reliabilities and prices for durable goods in an oligopoly[J]. European journal of operational research, 1999, 112(3):554-569.
[6] Lin Peichun, Shue L Y. Application of optimal control theory to product pricing and warranty with free replacement under the influence of basic lifetime distributions[J]. Computers & Industrial Engineering, 2005, 48(1):69-82.
[7] Huang Hongzhong, Liu Zhijie, Murthy D N P. Optimal reliability, warranty and price for new products[J]. ⅡE Transactions, 2007, 39(8):819-827.
[8] Jeyakumar K, Robert T P. Joint determination of price, warranty length and production quantity for new products under free warranty policy[J]. International Journal for Quality research, 2010, 4(1):51-58.
[9] 何平,曹开颖.基于质保期限和批发价的两制造商竞争问题[J]. 系统管理学报, 2016, 25(1):45-54.
[10] Jiang Bo, Zhang Xubing. How does a retailer's service plan affect a manufacturer's warranty[J]. Management Science, 2011, 57(4):727-740.
[11] Guajardo J A, Cohen M A, Netessine S. Service competition and product quality in the U.S.automobile industry[J]. Management Science, 2015,62(7):1860-1877.
[12] Bakshi N, Kim S H, Savva N.Signaling new product reliability with after-sales service contracts[J].Management Science,2015,61(8):1812-1819.
[13] 王轩, 刘丽文. 考虑维修服务质量的产品质保联合决策[J]. 中国管理科学,2016, 24(2):47-55.
[14] 王轩, 刘丽文. 静态市场下考虑重复购买的价格和质保期联合决策[J]. 中国管理科学, 2015, 23(4):70-77.
[15] 蒋紫艳, 赵军. 新产品定价决策的影响因素分析[J]. 运筹与管理, 2015,24(4):241-245.
[16] Jindal P. Risk preferences and demand drivers of extended warranties[J]. Marketing Science, 2014, 34(1):39-58.
[17] 严帅, 李四杰, 卞亦文. 基于质保服务的供应链契约协调机制[J]. 系统工程学报, 2013, 28(5):677-685.
[18] Xiao Tiaojun, Choi T M, Yang Danqin, et al. Service commitment strategy and pricing decisions in retail supply chains with risk-averse players[J].Service Science, 2015, 4(3):236-252.
[19] Chen Xu, Li Ling, Zhou Ming. Manufacturer's pricing strategy for supply chain with warranty period-dependent demand[J]. Omega, 2012, 40(6):807-816.
[20] 马建华, 艾兴政, 唐小我. 基于延保服务的竞争供应链纵向渠道结构选择[J]. 系统工程学报, 2015, 30(4):539-553.
[21] Mai D T, Liu Tieming, Morris M D S, et al. Quality coordination with extended warranty for store-brand products[J]. European Journal of Operational Research, 2016,256(2):524-532.
[22] Xie Jinhong, Sirbu M. Price competition and compatibility in the presence of positive demand externalities[J]. Management Science, 1995, 41(5):909-926.
