考虑策略消费者行为及模仿产品质量不确定的两竞争商定价
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摘要
基于策略消费者行为,在销售商1采用跨期定价销售新产品,以及销售商1和消费者均不知道之后销售的模仿产品确切质量的情形下,研究提供某新产品的销售商1和之后提供其模仿产品的销售商2之间的竞争性定价。分析了销售商1、销售商2和策略消费者三方之间的动态博弈,借助子博弈精炼纳什均衡,得到了新产品的最优跨期定价、模仿产品最优定价。研究发现,随着模仿产品质量增大,新产品销售商利润及新产品第二阶段价格均减小,第一阶段价格不变;模仿产品价格及其销售商利润随着模仿产品质量增大呈先增大后减小趋势;当模仿产品与新产品质量相同时,两产品的单位利润及模仿产品销售商的利润均为0。研究还发现,无论模仿产品的质量水平如何,凭借先动优势,作为主导者的销售商1所获利润总大于作为跟从者的销售商2所获利润。最后的数值模拟验证了所得结论的正确性。
When a new product is popular in the market, its imitated products begin to be sold quickly. Retailers and customers often do not know the exact quality of the imitated products. In order to cope with imitated products, the retailer of the new product always sell products at a discount when it learns the exact quality and the price of the imitated product.Based on strategic consumer behavior, we study the pricing problem of two competitive retailers in the case that Retailer 1 uses inter-temporal pricing policy. Both Retailer 1 and consumers don't know the exact imitated product quality before products are sold, where Retailer 1 offers a new product at the beginning of the sale and Retailer 2 offers an imitated product after a period of time. In addition, we researched the influence of different values of the imitation product quality on equilibrium prices and profits of Retailer 1 and Retailer 2. First of all, we analyze the optimal purchasing decisions of consumers with different valuation and dynamic game processes among strategic consumers. Retailer 1 and Retailer 2 define sub-game perfect Nash equilibrium of the game, and give the explanation of the sub-game perfect Nash equilibrium. The profit maximization function of Retailer 2 and that of Retailer 1 in period 1 and period 2 are respectively established by analyzing two sub-games. The optimal inter-temporal prices of the new product and the optimal price of the imitation product are obtained. Then the sub-game perfect Nash equilibrium of the game is derived, and the uniqueness of the equilibrium is proved. Second, the influence of different values of the imitated product quality on equilibrium prices and on the profits of Retailer 1 and Retailer 2 are also investigated. Finally, the correctness of conclusions is validated by numerical simulation. We find that the actual profit of Retailer 1 is not consistent with the expected profit when the imitated product quality is uncertain. Although the imitated product quality does not affect the expected profit of Retailer 1, it impacts the actual profit directly. It's not true that the higher the quality of the imitation product, the greater the profit of Retailer 2. With the increase of the imitated product quality, both the profit of Retailer 2 and the price of the imitated product first increase then decrease. Both the profit of Retailer 1 and the price of the new product in the second stage decrease, but the price in the first stage remains the same. Particularly, when the imitated product quality increases to the level of the new product, the price of the two products in the second stage equal to their cost, and Retailer 2 obtains zero profit. We also find that no matter what quality of the imitated product is, the profit of Retailer 1 as the leader is greater than that of Retailer 2 as the follower because of the monopoly advantage in the first stage and the first-mover advantage in the dynamic game between Retailer 1 and Retailer 2.
When a new product is popular in the market, its imitated products begin to be sold quickly. Retailers and customers often do not know the exact quality of the imitated products. In order to cope with imitated products, the retailer of the new product always sell products at a discount when it learns the exact quality and the price of the imitated product.Based on strategic consumer behavior, we study the pricing problem of two competitive retailers in the case that Retailer 1 uses inter-temporal pricing policy. Both Retailer 1 and consumers don't know the exact imitated product quality before products are sold, where Retailer 1 offers a new product at the beginning of the sale and Retailer 2 offers an imitated product after a period of time. In addition, we researched the influence of different values of the imitation product quality on equilibrium prices and profits of Retailer 1 and Retailer 2. First of all, we analyze the optimal purchasing decisions of consumers with different valuation and dynamic game processes among strategic consumers. Retailer 1 and Retailer 2 define sub-game perfect Nash equilibrium of the game, and give the explanation of the sub-game perfect Nash equilibrium. The profit maximization function of Retailer 2 and that of Retailer 1 in period 1 and period 2 are respectively established by analyzing two sub-games. The optimal inter-temporal prices of the new product and the optimal price of the imitation product are obtained. Then the sub-game perfect Nash equilibrium of the game is derived, and the uniqueness of the equilibrium is proved. Second, the influence of different values of the imitated product quality on equilibrium prices and on the profits of Retailer 1 and Retailer 2 are also investigated. Finally, the correctness of conclusions is validated by numerical simulation. We find that the actual profit of Retailer 1 is not consistent with the expected profit when the imitated product quality is uncertain. Although the imitated product quality does not affect the expected profit of Retailer 1, it impacts the actual profit directly. It's not true that the higher the quality of the imitation product, the greater the profit of Retailer 2. With the increase of the imitated product quality, both the profit of Retailer 2 and the price of the imitated product first increase then decrease. Both the profit of Retailer 1 and the price of the new product in the second stage decrease, but the price in the first stage remains the same. Particularly, when the imitated product quality increases to the level of the new product, the price of the two products in the second stage equal to their cost, and Retailer 2 obtains zero profit. We also find that no matter what quality of the imitated product is, the profit of Retailer 1 as the leader is greater than that of Retailer 2 as the follower because of the monopoly advantage in the first stage and the first-mover advantage in the dynamic game between Retailer 1 and Retailer 2.
引文
[1]Su X.Intertemporal pricing with strategic customer behavior[J].Management Science,2007,53(5):726-741.
[2]Gallego G,van Ryzin G.Optimal dynamic pricing of inventories with stochastic demand over finite[J].Management Science,1994,40(8):999-1020.
[3]Feng Y,Xiao B.A continuous-time yield management model with multiple prices and reversible price changes[J].Management Science,2000,46(5):644-657.
[4]Gallego G,van Ryzin G.A multiproduct dynamic pricing problem and its application to network yield management[J].Oper.Res.1997,45(1):24-41.
[5]Akcay Y,Natarajan HP,Xu SH.Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice[J].Management science,2010,56(8):1345-1361.
[6]Dong L,Kouvelis P,Tian Z.Dynamic pricing and inventory control of substitute products[J].Manufacturing Service Oper.Management,2009,11(2):317-339.
[7]Dasci A,Karakul M.Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly[J].European Journal of Operational Research,2009,197(3):945-968.
[8]Xu X,Hopp W.A monopolistic and oligopolistic stochastic flow revenue management model[J].Oper.Res,2006,54(6):1098-1109.
[9]Aviv Y,Pazgal A.Optimal pricing of seasonal products in the presence of forward-looking customers[J].Manufacturing Service Oper.Management,2008,10(3):339-359.
[10]Besanko D,Winston WL.Optimal price skimming by a monopolist facing rational consumers[J].ManagementScience,1990,36(5):555-567.
[11]Yu,M.,Ahn HS,Kapuscinski R.Rationing Capacity in Advance Selling to Signal Quality[J].Management Science,2015,61(3):560-577.
[12]Su,X.,Z.J.Max Shen.Customer Behavior Modeling in Revenue Management and Auctions:A Review and New Research Opportunities[J].Production and Operations Management,2007,16(6):713-728.
[13]毕功兵,王怡璇,丁晶晶.存在替代品情况下考虑消费者策略行为的跨期定价[J],系统工程学报,2013,28(1):47-54.
[14]Parlaktrk AK.The value of product variety when selling to strategic consumers[J].Manufacturing Service Oper.Management,2012,4(3):371-385.
[15]Liang C,?akany?ld?r?m M,Sethi SP.Analysis of Product Rollover Strategies in the Presence of Strategic Customers[J].Management Science,2014,60(4):1033-1056.
[16]Levin Y,McGill J,Nediak M.Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition[J].Management Science,2009,55(1):32-46.
[17]Liu Q,Zhang D.Dynamic Pricing Competition with Strategic Customers Under Vertical Product Differentiation[J].Management Science,2013,59(1):371-385.
(1)这里c是消费者估价分布区间[0,M]单位化为[0,1]后对应的值,即c=产品实际成本/M,此变换不影响文中结论成立。
[2]Gallego G,van Ryzin G.Optimal dynamic pricing of inventories with stochastic demand over finite[J].Management Science,1994,40(8):999-1020.
[3]Feng Y,Xiao B.A continuous-time yield management model with multiple prices and reversible price changes[J].Management Science,2000,46(5):644-657.
[4]Gallego G,van Ryzin G.A multiproduct dynamic pricing problem and its application to network yield management[J].Oper.Res.1997,45(1):24-41.
[5]Akcay Y,Natarajan HP,Xu SH.Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice[J].Management science,2010,56(8):1345-1361.
[6]Dong L,Kouvelis P,Tian Z.Dynamic pricing and inventory control of substitute products[J].Manufacturing Service Oper.Management,2009,11(2):317-339.
[7]Dasci A,Karakul M.Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly[J].European Journal of Operational Research,2009,197(3):945-968.
[8]Xu X,Hopp W.A monopolistic and oligopolistic stochastic flow revenue management model[J].Oper.Res,2006,54(6):1098-1109.
[9]Aviv Y,Pazgal A.Optimal pricing of seasonal products in the presence of forward-looking customers[J].Manufacturing Service Oper.Management,2008,10(3):339-359.
[10]Besanko D,Winston WL.Optimal price skimming by a monopolist facing rational consumers[J].ManagementScience,1990,36(5):555-567.
[11]Yu,M.,Ahn HS,Kapuscinski R.Rationing Capacity in Advance Selling to Signal Quality[J].Management Science,2015,61(3):560-577.
[12]Su,X.,Z.J.Max Shen.Customer Behavior Modeling in Revenue Management and Auctions:A Review and New Research Opportunities[J].Production and Operations Management,2007,16(6):713-728.
[13]毕功兵,王怡璇,丁晶晶.存在替代品情况下考虑消费者策略行为的跨期定价[J],系统工程学报,2013,28(1):47-54.
[14]Parlaktrk AK.The value of product variety when selling to strategic consumers[J].Manufacturing Service Oper.Management,2012,4(3):371-385.
[15]Liang C,?akany?ld?r?m M,Sethi SP.Analysis of Product Rollover Strategies in the Presence of Strategic Customers[J].Management Science,2014,60(4):1033-1056.
[16]Levin Y,McGill J,Nediak M.Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition[J].Management Science,2009,55(1):32-46.
[17]Liu Q,Zhang D.Dynamic Pricing Competition with Strategic Customers Under Vertical Product Differentiation[J].Management Science,2013,59(1):371-385.
(1)这里c是消费者估价分布区间[0,M]单位化为[0,1]后对应的值,即c=产品实际成本/M,此变换不影响文中结论成立。
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