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## Optimal pricing strategy in a dual-channel supply chain: A two-period game analysis

 1 School of Business Administration, Hunan University, Hunan 410082, China 2 Supply Chain and Logistics Optimization Research Centre, Department of Mechanical, Automotive & Materials Engineering, University of Windsor, Ontario N9B 3P4, Canada

*Corresponding author: Guoqing Zhang

Received  October 2021 Revised  March 2022 Early access April 2022

With the development of e-commerce and the rapid updating of products, multi-period pricing has been widely attempted in dual-channel supply chains. In this paper, we develop a two-period game-theoretical model to investigate the problem of two-period pricing and strategy choice for a dual-channel supply chain in which a manufacturer sells a product through its direct channel and an independent retailer. The two common pricing strategies, i.e., dynamic pricing and preannounced pricing, are considered. Through analyzing and comparing, we derive a unique Stackelberg equilibrium under the two pricing strategies and find that dynamic pricing dominates preannounced pricing and achieves a win-win result for the retailer and the manufacturer. Moreover, under this strategy, the manufacturer charges a higher or lower direct price in the second period than in the first period depending on channel competition, whereas the retailer always set a lower retail price in the second period. Finally, we extend our models to consider a unique wholesale pricing strategy, the profit discount factor, and different decision sequences for the selling prices of the two channels. We show that our main results are robust, except that the decision sequence changes the optimal pricing strategy choice of the retailer.

Citation: Haijiao Li, Kuan Yang, Guoqing Zhang. Optimal pricing strategy in a dual-channel supply chain: A two-period game analysis. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022072
##### References:
 [1] Y. Aviv, M. M. Wei and F. Q. Zhang, Responsive pricing of fashion products: The effects of demand learning and strategic consumer behavior, Manage. Sci., 65 (2019), 2982-3000. [2] G. Berbeglia, G. Rayaprolu and A. Vetta, Pricing policies for selling indivisible storable goods to strategic consumers, Ann. Oper. Res., 274 (2019), 131-154.  doi: 10.1007/s10479-018-2916-x. [3] G. P. Cachon and R. Swinney, Purchasing, pricing, and quick response in the presence of strategic consumers, Manage. Sci., 55 (2009), 497-511. [4] G. G. Cai, Channel selection and coordination in dual-channel supply chains, J. Retail., 86 (2010), 22-36. [5] Z. H. Cao and J. Min, Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain, J. Ind. Manag. Optim., 18 (2022), 541-560.  doi: 10.3934/jimo.2020167. [6] K. Cattani, W. Gilland, H. S. Heese and J. Swaminathan, Boiling frogs: Pricing strategies for a manufacturer adding a direct channel that competes with the traditional channel, Prod. Oper. Manag., 15 (2006), 40-56. [7] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. [8] J. X. Chen, L. Liang, D. Q. Yao and S. G. Sun, Price and quality decisions in dual-channel supply chains, Eur. J. Oper. Res., 259 (2017), 935-948.  doi: 10.1016/j.ejor.2016.11.016. [9] K. Chen, H. J. Zhou and D. Lei, Two-period pricing and ordering decisions of perishable products with a learning period for demand disruption, J. Ind. Manag. Optim., 17 (2021), 3131-3163.  doi: 10.3934/jimo.2020111. [10] K. H. Chen, Y. Zha, L. C. Alwan and L. Zhang, Dynamic pricing in the presence of reference price effect and consumer strategic behaviour, Int. J. Prod. Res., 58 (2019), 546-561. [11] W. K. Chiang, D. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Manage. Sci., 49 (2003), 1-20. [12] J. Correa, R. Montoya and C. Thraves, Contingent preannounced pricing policies with strategic consumers, Oper. Res., 64 (2016), 251-272.  doi: 10.1287/opre.2015.1452. [13] S. Dasu and C. Tong, Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes, Eur. J. Oper. Res., 204 (2010), 662-671. [14] J. F. Dong and D. D. Wu, Two-period pricing and quick response with strategic customers, Int. J. Prod. Econ., 215 (2019), 165-173. [15] W. Elmaghraby, A. Gülcü and P. Keskinocak, Designing optimal preannounced markdowns in the presence of rational customers with multiunit demands, Manuf. Serv. Oper. Manag., 10 (2008), 126-148. [16] W. Elmaghraby, S. A. Lippman, C. S. Tang and R. Yin, Pre-announced pricing strategies with reservations, Prod. Oper. Manag., 18 (2009), 381-401. [17] J. Feng, X. Li and X. Q. Zhang, Online product reviews-triggered dynamic pricing: Theory and evidence, Inf. Syst. Res., 30 (2019), 1107-1123. [18] I. Kana, Uniqlo Pricing U-Turn Pays off... for Now, Financial Times, 2016. Available from: https://www.ft.com/content/0a52b84a-514e-11e6-8852-6a398efc4350. [19] O. Kaya and H. Bayer, Pricing and lot-sizing decisions for perishable products when demand changes by freshness, J. Ind. Manag. Optim., 17 (2021), 3113-3129.  doi: 10.3934/jimo.2020110. [20] Q. Lei, J. He, C. Ma and Z. L. Jin, The impact of consumer behavior on preannounced pricing for a dual-channel supply chain, Int. Trans. Oper. Res., 27 (2020), 2949-2975.  doi: 10.1111/itor.12786. [21] Y. Levin, J. McGill and M. Nediak, Dynamic pricing in the presence of strategic consumers and oligopolistic competition, Manage. Sci., 55 (2009), 32-46. [22] J. Li, L. Yi, V. Shi and X. D. Chen, Supplier encroachment strategy in the presence of retail strategic inventory: Centralization or decentralization?, Omega, 98 (2021), 102213. [23] J. C. Liu, X. Zhai and L. H. Chen, Optimal pricing strategy under trade-in program in the presence of strategic consumers, Omega, 84 (2019), 1-17. [24] T. Maiti and B. C. Giri, Two-period pricing and decision strategies in a two-echelon supply chain under price-dependent demand, Appl. Math. Model., 42 (2017), 655-674.  doi: 10.1016/j.apm.2016.10.051. [25] K. Matsui, Should a retailer bargain over a wholesale price with a manufacturer using a dual-channel supply chain?, Eur. J. Oper. Res., 300 (2022), 1050-1066.  doi: 10.1016/j.ejor.2021.09.012. [26] N. M. Modak and P. Kelle, Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand, Eur. J. Oper. Res., 272 (2019), 147-161.  doi: 10.1016/j.ejor.2018.05.067. [27] Y. Papanastasiou and N. Savva, Dynamic pricing in the presence of social learning and strategic consumers, Manage. Sci., 63 (2017), 919-939. [28] M. Radhi and G. Q. Zhang, Pricing policies for a dual-channel retailer with cross-channel returns, Comput. Ind. Eng., 119 (2018), 63-75. [29] M. Spence, Product differentiation and welfare, Am. Econ. Rev., 66 (1976), 407-414. [30] N. L. Stokey, Intertemporal price discrimination, Q. J. Econ., 93 (1979), 355-371. [31] H. X. Sun, Y. Wan, Y. Li, L. L. Zhang and Z. Zhou, Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours, J. Ind. Manag. Optim., 17 (2021), 601-631.  doi: 10.3934/jimo.2019125. [32] L. B. Sun, X. T. Jiao, X. L. Guo and Y. G. Yu, Pricing policies in dual distribution channels: The reference effect of official prices, Eur. J. Oper. Res., 296 (2022), 146-157.  doi: 10.1016/j.ejor.2021.03.040. [33] B. Tedeschi, Compressed Data; Big Companies Go Slowly in Devising Net Strategy, New York Times, 2000. Available from: https://www.nytimes.com/2000/03/27/business/compressed-data-big-companies-go-slowly-in-devising-net-strategy.html. [34] H. Wu, G. G. Cai, J. Chen and C. Sheu, Online manufacturer referral to heterogeneous retailers, Prod. Oper. Manag., 24 (2015), 1768-1782. [35] Y. Xiong, W. Yan, K. Fernandes, Z. K. Xiong and N. Guo, "Bricks vs. Clicks": The impact of manufacturer encroachment with a dealer leasing and selling of durable goods, Eur. J. Oper. Res., 217 (2012), 75-83.  doi: 10.1016/j.ejor.2011.08.012. [36] G. Y. Xu, B. Dan, X. M. Zhang and C. Liu, Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contrac, Int. J. Prod. Econ., 147 (2014), 171-179. [37] M. S. Xue and G. W. Zhu, Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items, J. Ind. Manag. Optim., 17 (2021), 633-648.  doi: 10.3934/jimo.2019126. [38] W. Yan, Y. Xiong, J. H. Chu, G. D. Li and Z. K. Xiong, Clicks versus Bricks: The role of durability in marketing channel strategy of durable goods manufacturers, Eur. J. Oper. Res., 265 (2018), 909-918.  doi: 10.1016/j.ejor.2017.08.039. [39] W. J. Yang, J. T. Zhang and H. Yan, Impacts of online consumer reviews on a dual-channel supply chain, Omega, 101 (2020), 102266. [40] X. D. Yang, G. G. Cai, C. A. Ingene and J. H. Zhang, Manufacturer strategy on service provision in competitive channels, Prod. Oper. Manag., 29 (2020), 72-89. [41] R. Yin, Y. Aviv, A. Pazgal and C. S. Tang, Optimal markdown pricing: Implications of inventory display formats in the presence of strategic customers, Manage. Sci., 55 (2009), 1391-1408. [42] M. Yu, L. Debo and R. Kapuscinski, Strategic waiting for consumer-generated quality information: Dynamic pricing of new experience goods, Manage. Sci., 62 (2016), 410-435. [43] C. Zhang, Y. Liu and G. H. Han, Two-stage pricing strategies of a dual-channel supply chain considering public green preference, Comput. Ind. Eng., 151 (2021), 106988. [44] J. X. Zhang, S. Li, S. C. Zhang and R. Dai, Manufacturer encroachment with quality decision under asymmetric demand information, Eur. J. Oper. Res., 273 (2019), 217-236.  doi: 10.1016/j.ejor.2018.08.002. [45] J. H. Zhou, R. J. Zhao and B. Wang, Behavior-based price discrimination in a dual-channel supply chain with retailer's information disclosure, Electron. Commer. Res. Appl., 39 (2020), 100916. [46] Y. W. Zhou, J. S. Guo and W. H. Zhou, Pricing/service strategies for a dual-channel supply chain with free riding and service-cost sharing, Int. J. Prod. Econ., 196 (2018), 198-210. [47] B. L. Zhu, B. Wen, S. F. Ji and R. Z. Qiu, Coordinating a dual-channel supply chain with conditional value-at-risk under uncertainties of yield and demand, Comput. Ind. Eng., 139 (2020), 106181.

show all references

##### References:
 [1] Y. Aviv, M. M. Wei and F. Q. Zhang, Responsive pricing of fashion products: The effects of demand learning and strategic consumer behavior, Manage. Sci., 65 (2019), 2982-3000. [2] G. Berbeglia, G. Rayaprolu and A. Vetta, Pricing policies for selling indivisible storable goods to strategic consumers, Ann. Oper. Res., 274 (2019), 131-154.  doi: 10.1007/s10479-018-2916-x. [3] G. P. Cachon and R. Swinney, Purchasing, pricing, and quick response in the presence of strategic consumers, Manage. Sci., 55 (2009), 497-511. [4] G. G. Cai, Channel selection and coordination in dual-channel supply chains, J. Retail., 86 (2010), 22-36. [5] Z. H. Cao and J. Min, Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain, J. Ind. Manag. Optim., 18 (2022), 541-560.  doi: 10.3934/jimo.2020167. [6] K. Cattani, W. Gilland, H. S. Heese and J. Swaminathan, Boiling frogs: Pricing strategies for a manufacturer adding a direct channel that competes with the traditional channel, Prod. Oper. Manag., 15 (2006), 40-56. [7] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. [8] J. X. Chen, L. Liang, D. Q. Yao and S. G. Sun, Price and quality decisions in dual-channel supply chains, Eur. J. Oper. Res., 259 (2017), 935-948.  doi: 10.1016/j.ejor.2016.11.016. [9] K. Chen, H. J. Zhou and D. Lei, Two-period pricing and ordering decisions of perishable products with a learning period for demand disruption, J. Ind. Manag. Optim., 17 (2021), 3131-3163.  doi: 10.3934/jimo.2020111. [10] K. H. Chen, Y. Zha, L. C. Alwan and L. Zhang, Dynamic pricing in the presence of reference price effect and consumer strategic behaviour, Int. J. Prod. Res., 58 (2019), 546-561. [11] W. K. Chiang, D. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Manage. Sci., 49 (2003), 1-20. [12] J. Correa, R. Montoya and C. Thraves, Contingent preannounced pricing policies with strategic consumers, Oper. Res., 64 (2016), 251-272.  doi: 10.1287/opre.2015.1452. [13] S. Dasu and C. Tong, Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes, Eur. J. Oper. Res., 204 (2010), 662-671. [14] J. F. Dong and D. D. Wu, Two-period pricing and quick response with strategic customers, Int. J. Prod. Econ., 215 (2019), 165-173. [15] W. Elmaghraby, A. Gülcü and P. Keskinocak, Designing optimal preannounced markdowns in the presence of rational customers with multiunit demands, Manuf. Serv. Oper. Manag., 10 (2008), 126-148. [16] W. Elmaghraby, S. A. Lippman, C. S. Tang and R. Yin, Pre-announced pricing strategies with reservations, Prod. Oper. Manag., 18 (2009), 381-401. [17] J. Feng, X. Li and X. Q. Zhang, Online product reviews-triggered dynamic pricing: Theory and evidence, Inf. Syst. Res., 30 (2019), 1107-1123. [18] I. Kana, Uniqlo Pricing U-Turn Pays off... for Now, Financial Times, 2016. Available from: https://www.ft.com/content/0a52b84a-514e-11e6-8852-6a398efc4350. [19] O. Kaya and H. Bayer, Pricing and lot-sizing decisions for perishable products when demand changes by freshness, J. Ind. Manag. Optim., 17 (2021), 3113-3129.  doi: 10.3934/jimo.2020110. [20] Q. Lei, J. He, C. Ma and Z. L. Jin, The impact of consumer behavior on preannounced pricing for a dual-channel supply chain, Int. Trans. Oper. Res., 27 (2020), 2949-2975.  doi: 10.1111/itor.12786. [21] Y. Levin, J. McGill and M. Nediak, Dynamic pricing in the presence of strategic consumers and oligopolistic competition, Manage. Sci., 55 (2009), 32-46. [22] J. Li, L. Yi, V. Shi and X. D. Chen, Supplier encroachment strategy in the presence of retail strategic inventory: Centralization or decentralization?, Omega, 98 (2021), 102213. [23] J. C. Liu, X. Zhai and L. H. Chen, Optimal pricing strategy under trade-in program in the presence of strategic consumers, Omega, 84 (2019), 1-17. [24] T. Maiti and B. C. Giri, Two-period pricing and decision strategies in a two-echelon supply chain under price-dependent demand, Appl. Math. Model., 42 (2017), 655-674.  doi: 10.1016/j.apm.2016.10.051. [25] K. Matsui, Should a retailer bargain over a wholesale price with a manufacturer using a dual-channel supply chain?, Eur. J. Oper. Res., 300 (2022), 1050-1066.  doi: 10.1016/j.ejor.2021.09.012. [26] N. M. Modak and P. Kelle, Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand, Eur. J. Oper. Res., 272 (2019), 147-161.  doi: 10.1016/j.ejor.2018.05.067. [27] Y. Papanastasiou and N. Savva, Dynamic pricing in the presence of social learning and strategic consumers, Manage. Sci., 63 (2017), 919-939. [28] M. Radhi and G. Q. Zhang, Pricing policies for a dual-channel retailer with cross-channel returns, Comput. Ind. Eng., 119 (2018), 63-75. [29] M. Spence, Product differentiation and welfare, Am. Econ. Rev., 66 (1976), 407-414. [30] N. L. Stokey, Intertemporal price discrimination, Q. J. Econ., 93 (1979), 355-371. [31] H. X. Sun, Y. Wan, Y. Li, L. L. Zhang and Z. Zhou, Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours, J. Ind. Manag. Optim., 17 (2021), 601-631.  doi: 10.3934/jimo.2019125. [32] L. B. Sun, X. T. Jiao, X. L. Guo and Y. G. Yu, Pricing policies in dual distribution channels: The reference effect of official prices, Eur. J. Oper. Res., 296 (2022), 146-157.  doi: 10.1016/j.ejor.2021.03.040. [33] B. Tedeschi, Compressed Data; Big Companies Go Slowly in Devising Net Strategy, New York Times, 2000. Available from: https://www.nytimes.com/2000/03/27/business/compressed-data-big-companies-go-slowly-in-devising-net-strategy.html. [34] H. Wu, G. G. Cai, J. Chen and C. Sheu, Online manufacturer referral to heterogeneous retailers, Prod. Oper. Manag., 24 (2015), 1768-1782. [35] Y. Xiong, W. Yan, K. Fernandes, Z. K. Xiong and N. Guo, "Bricks vs. Clicks": The impact of manufacturer encroachment with a dealer leasing and selling of durable goods, Eur. J. Oper. Res., 217 (2012), 75-83.  doi: 10.1016/j.ejor.2011.08.012. [36] G. Y. Xu, B. Dan, X. M. Zhang and C. Liu, Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contrac, Int. J. Prod. Econ., 147 (2014), 171-179. [37] M. S. Xue and G. W. Zhu, Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items, J. Ind. Manag. Optim., 17 (2021), 633-648.  doi: 10.3934/jimo.2019126. [38] W. Yan, Y. Xiong, J. H. Chu, G. D. Li and Z. K. Xiong, Clicks versus Bricks: The role of durability in marketing channel strategy of durable goods manufacturers, Eur. J. Oper. Res., 265 (2018), 909-918.  doi: 10.1016/j.ejor.2017.08.039. [39] W. J. Yang, J. T. Zhang and H. Yan, Impacts of online consumer reviews on a dual-channel supply chain, Omega, 101 (2020), 102266. [40] X. D. Yang, G. G. Cai, C. A. Ingene and J. H. Zhang, Manufacturer strategy on service provision in competitive channels, Prod. Oper. Manag., 29 (2020), 72-89. [41] R. Yin, Y. Aviv, A. Pazgal and C. S. Tang, Optimal markdown pricing: Implications of inventory display formats in the presence of strategic customers, Manage. Sci., 55 (2009), 1391-1408. [42] M. Yu, L. Debo and R. Kapuscinski, Strategic waiting for consumer-generated quality information: Dynamic pricing of new experience goods, Manage. Sci., 62 (2016), 410-435. [43] C. Zhang, Y. Liu and G. H. Han, Two-stage pricing strategies of a dual-channel supply chain considering public green preference, Comput. Ind. Eng., 151 (2021), 106988. [44] J. X. Zhang, S. Li, S. C. Zhang and R. Dai, Manufacturer encroachment with quality decision under asymmetric demand information, Eur. J. Oper. Res., 273 (2019), 217-236.  doi: 10.1016/j.ejor.2018.08.002. [45] J. H. Zhou, R. J. Zhao and B. Wang, Behavior-based price discrimination in a dual-channel supply chain with retailer's information disclosure, Electron. Commer. Res. Appl., 39 (2020), 100916. [46] Y. W. Zhou, J. S. Guo and W. H. Zhou, Pricing/service strategies for a dual-channel supply chain with free riding and service-cost sharing, Int. J. Prod. Econ., 196 (2018), 198-210. [47] B. L. Zhu, B. Wen, S. F. Ji and R. Z. Qiu, Coordinating a dual-channel supply chain with conditional value-at-risk under uncertainties of yield and demand, Comput. Ind. Eng., 139 (2020), 106181.
Decision sequence under dynamic pricing strategy
Decision sequence under preannounced pricing strategy
Impact of channel substitutability on prices
Impact of channel substitutability on profits
Decision sequence under a unique wholesale pricing strategy
Impact of $\theta$ on profits under unique wholesale pricing strategy
Impact of $\delta$ on profits
Direct price is determined after retail price
Direct price and retail price are determined simultaneously
Impact of $\theta$ on profits under different decision timings
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