{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T20:04:37Z","timestamp":1774037077910,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T00:00:00Z","timestamp":1746576000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Major Project of Philosophy and Social Science Research in Hubei Province Higher Education Institutions","award":["22ZD046"],"award-info":[{"award-number":["22ZD046"]}]},{"name":"The Major Project of Philosophy and Social Science Research in Hubei Province Higher Education Institutions","award":["2022H20537"],"award-info":[{"award-number":["2022H20537"]}]},{"name":"The Major Project of Philosophy and Social Science Research in Hubei Province Higher Education Institutions","award":["2023H10254"],"award-info":[{"award-number":["2023H10254"]}]},{"name":"The Major Project of Philosophy and Social Science Research in Hubei Province Higher Education Institutions","award":["2024H10109"],"award-info":[{"award-number":["2024H10109"]}]},{"name":"The Major Project of Philosophy and Social Science Research in Hubei Province Higher Education Institutions","award":["2024H10143"],"award-info":[{"award-number":["2024H10143"]}]},{"name":"The Major Project of Philosophy and Social Science Research in Hubei Province Higher Education Institutions","award":["2024H20281"],"award-info":[{"award-number":["2024H20281"]}]},{"name":"The Major Project of Philosophy and Social Science Research in Hubei Province Higher Education Institutions","award":["20211102"],"award-info":[{"award-number":["20211102"]}]},{"name":"The Wuhan University of Science &amp; Technology Research Project","award":["22ZD046"],"award-info":[{"award-number":["22ZD046"]}]},{"name":"The Wuhan University of Science &amp; Technology Research Project","award":["2022H20537"],"award-info":[{"award-number":["2022H20537"]}]},{"name":"The Wuhan University of Science &amp; Technology Research Project","award":["2023H10254"],"award-info":[{"award-number":["2023H10254"]}]},{"name":"The Wuhan University of Science &amp; Technology Research Project","award":["2024H10109"],"award-info":[{"award-number":["2024H10109"]}]},{"name":"The Wuhan University of Science &amp; Technology Research Project","award":["2024H10143"],"award-info":[{"award-number":["2024H10143"]}]},{"name":"The Wuhan University of Science &amp; Technology Research Project","award":["2024H20281"],"award-info":[{"award-number":["2024H20281"]}]},{"name":"The Wuhan University of Science &amp; Technology Research Project","award":["20211102"],"award-info":[{"award-number":["20211102"]}]},{"name":"The Department of Education of Hubei Province Young and Middle-Aged Talents Project","award":["22ZD046"],"award-info":[{"award-number":["22ZD046"]}]},{"name":"The Department of Education of Hubei Province Young and Middle-Aged Talents Project","award":["2022H20537"],"award-info":[{"award-number":["2022H20537"]}]},{"name":"The Department of Education of Hubei Province Young and Middle-Aged Talents Project","award":["2023H10254"],"award-info":[{"award-number":["2023H10254"]}]},{"name":"The Department of Education of Hubei Province Young and Middle-Aged Talents Project","award":["2024H10109"],"award-info":[{"award-number":["2024H10109"]}]},{"name":"The Department of Education of Hubei Province Young and Middle-Aged Talents Project","award":["2024H10143"],"award-info":[{"award-number":["2024H10143"]}]},{"name":"The Department of Education of Hubei Province Young and Middle-Aged Talents Project","award":["2024H20281"],"award-info":[{"award-number":["2024H20281"]}]},{"name":"The Department of Education of Hubei Province Young and Middle-Aged Talents Project","award":["20211102"],"award-info":[{"award-number":["20211102"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>This paper explores how to reduce supply-demand conflicts in supply chains by utilizing complementary products\u2019 unique relationships and shared objectives. Also, it considers the service level concerns of consumers. Primarily employing game theory, this paper analyzes the pricing strategies of complementary products within a three-tier dual-channel supply chain, the relationship between pricing and service levels, and the performance optimization across channels. Numerical results demonstrate that elevated values of \u03b11 indicate heightened consumer sensitivity to manufacturer price fluctuations. To sustain sales volume, manufacturers are compelled to reduce prices, consequently leading to a decline in equilibrium prices within the market. A rise in \u03b21 induces an across-the-board increase in all price tiers, albeit with differential magnitudes. The intensification of channel competition \u03b12 exerts downward pressure on all pricing components. The retailer\u2019s price demonstrates maximal responsiveness to \u03b22 fluctuations, as retailers directly absorb cost variances.<\/jats:p>","DOI":"10.3390\/systems13050360","type":"journal-article","created":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T11:46:19Z","timestamp":1746618379000},"page":"360","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Decision-Making in Complementary Products Supply Chain: Game Theory and Sensitivity Analysis"],"prefix":"10.3390","volume":"13","author":[{"given":"Jiashu","family":"Cai","sequence":"first","affiliation":[{"name":"School of Physics and Mechanics, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5737-5135","authenticated-orcid":false,"given":"Yong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Management, Wuhan University of Science and Technology, Wuhan 430080, China"},{"name":"Department of Production Engineering, KTH Royal Institute of Technology, 114 28 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9694-0483","authenticated-orcid":false,"given":"Xi","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Production Engineering, KTH Royal Institute of Technology, 114 28 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiamin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Management, Wuhan University of Science and Technology, Wuhan 430080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8679-8049","authenticated-orcid":false,"given":"Lihui","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Production Engineering, KTH Royal Institute of Technology, 114 28 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102675","DOI":"10.1016\/j.tre.2022.102675","article-title":"Optimal Decisions of Modularity, Prices and Return Policy in a Dual-Channel Supply Chain Under Mass Customization","volume":"160","author":"Wang","year":"2022","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102088","DOI":"10.1016\/j.pacfin.2023.102088","article-title":"Digital Transformation Along the Supply Chain","volume":"80","author":"Guo","year":"2023","journal-title":"Pac.-Basin Financ. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.tre.2015.11.007","article-title":"Pricing Strategies of a Dual-Channel Supply Chain with Risk Aversion","volume":"90","author":"Liu","year":"2016","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1016\/j.ejor.2020.08.002","article-title":"Joint pricing and Inventory Decisions for Substitutable and Perishable Products under demand uncertainty","volume":"293","author":"Fang","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7471","DOI":"10.1080\/00207543.2020.1765040","article-title":"Decisions and Coordination of Green E-Commerce Supply Chain Considering Green Manufacturer\u2019s Fairness Concerns","volume":"58","author":"Wang","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"ref_6","first-page":"3841","article-title":"Products Pricing and Return Strategies for the Dual Channel Retailers","volume":"22","author":"Liu","year":"2022","journal-title":"Oper. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"100916","DOI":"10.1016\/j.elerap.2019.100916","article-title":"Behavior-Based Price Discrimination in a Dual-Channel Supply Chain with Retailer\u2019s Information Disclosure","volume":"39","author":"Zhou","year":"2020","journal-title":"Electron. Commer. Res. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2440001","DOI":"10.1142\/S0217595924400013","article-title":"Strategic Technology Innovation of a Basic Product in an E-Commerce Platform Supply Chain with a Potential Entrant in a Complementary Goods Market","volume":"41","author":"Shang","year":"2024","journal-title":"Asia-Pac. J. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2045842","DOI":"10.1155\/2024\/2045842","article-title":"Research on Nash Equilibrium of Dual-Channel Supply Chain Based on Wholesale Price Discrimination and Sales Efforts","volume":"2024","author":"Sha","year":"2024","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hamzaoui, A.F., Turki, S., and Rezg, N. (2024). Efficient Strategic Pricing in a Dual-Channel Stackelberg Supply Chain: Incorporating Remanufacturing and Sales Commissions Across Multiple Periods. Appl. Sci., 14.","DOI":"10.3390\/app14104180"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1080\/07408170590885594","article-title":"Competitive Stocking and Coordination in a Multiple-Channel Distribution System","volume":"37","author":"Boyaci","year":"2005","journal-title":"IIE Trans."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.ejor.2024.09.027","article-title":"Existence of Equilibrium in a Dynamic Supply Chain Game with Vertical Coordination, Horizontal Competition, and Complementary Goods","volume":"321","author":"Crettez","year":"2025","journal-title":"Eur. J. Oper. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.ejor.2021.02.052","article-title":"Coordinating a Closed Loop Supply Chain with Fairness Concern by a Constant Wholesale Price Contract","volume":"295","author":"Sarkar","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"ref_14","first-page":"57","article-title":"Dual-Channel Supply Chain Pricing Decisions for Low-Carbon Consumers: A Review","volume":"2","author":"Song","year":"2023","journal-title":"J. Intell. Manag. Decis."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"110204","DOI":"10.1016\/j.cie.2024.110204","article-title":"Game Theoretical Analysis in Two-Echelon Sustainable Supply Chains to Manage and Coordinate Strategic Decisions","volume":"192","author":"Modak","year":"2024","journal-title":"Comput. Ind. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6633","DOI":"10.1080\/00207543.2020.1821929","article-title":"Revenue-Sharing Contracts in Supply Chains: A Comprehensive Literature Review","volume":"59","author":"Bart","year":"2021","journal-title":"Int. J. Prod. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"108322","DOI":"10.1016\/j.ijpe.2021.108322","article-title":"A Consignment Contract with Revenue Sharing Between an App Developer and a Distribution Platform","volume":"243","author":"Avinadav","year":"2022","journal-title":"Int. J. Prod. Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1080\/10864415.2020.1715530","article-title":"Direct Selling, Reselling, or Agency Selling? Manufacturer\u2019s Online Distribution Strategies and Their Impact","volume":"24","author":"Pu","year":"2020","journal-title":"Int. J. Electron. Commer."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"103278","DOI":"10.1016\/j.jinteco.2019.103278","article-title":"One Way to the Top: How Services Boost the Demand for Goods","volume":"123","author":"Ariu","year":"2020","journal-title":"J. Int. Econ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.ejor.2019.08.026","article-title":"Strategic Contracting and Hybrid Use of Agency and Wholesale Contracts in E-Commerce Platforms","volume":"281","author":"Zennyo","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_21","first-page":"46","article-title":"Sourcing and Bundling Decisions for Complementary Products in the Presence of Supply Disruption","volume":"12","author":"Hemmati","year":"2025","journal-title":"J. Manag. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1007\/s10479-021-03945-0","article-title":"Disclosure of Quality Preference-Revealing Information in a Supply Chain with Competitive Products","volume":"329","author":"Sun","year":"2023","journal-title":"Ann. Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"121447","DOI":"10.1016\/j.eswa.2023.121447","article-title":"Competitive pricing of complementary telecommunication services with subscriber churn in a duopoly","volume":"237","author":"Soltani","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s10479-022-04909-8","article-title":"Reverse Supply Chain Management with Dual Channel and Collection Disruptions: Supply Chain Coordination and Game Theory Approaches","volume":"324","author":"Johari","year":"2023","journal-title":"Ann. Oper. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"108515","DOI":"10.1016\/j.cie.2022.108515","article-title":"Pricing strategy in a dual-channel supply chain with overconfident consumers","volume":"172","author":"Liu","year":"2022","journal-title":"Comput. Ind. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"109018","DOI":"10.1016\/j.cie.2023.109018","article-title":"Separate and bundling selling strategies for complementary products in a participative pricing mechanism","volume":"177","author":"Hemmati","year":"2023","journal-title":"Comput. Ind. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.ejor.2020.09.031","article-title":"Competition in dual-channel supply chains: The manufacturers\u2019 channel selection","volume":"291","author":"Zhang","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1007\/s10479-020-03895-z","article-title":"A structural mathematical model on two echelon supply chain system","volume":"315","author":"Sana","year":"2022","journal-title":"Ann. Oper. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2314659","DOI":"10.1155\/2020\/2314659","article-title":"Complementary Product Pricing and Service Cooperation Strategy in a Dual-Channel Supply Chain","volume":"2020","author":"Ren","year":"2020","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"He, Q., Zhang, T., Wang, J., and Li, J. (2024). Dual-Channel Supply Chain Pricing Coordination and Channel Selection with Reference Quality Effect Under Blockchain Traceability. Symmetry, 16.","DOI":"10.3390\/sym16121650"},{"key":"ref_31","first-page":"198","article-title":"Dual-Channel Supply Chain Coordination Considering the Consumer\u2019s Perception of Quality","volume":"58","author":"Haiju","year":"2024","journal-title":"Econ. Comput. Econ. Cybern. Stud. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"103706","DOI":"10.1016\/j.jretconser.2024.103706","article-title":"Analytical Insights into Coordination and Competition in Dual-Channel Supply Chains: A Multi-Factor Dependent Demand Perspective","volume":"78","author":"Nematollahi","year":"2024","journal-title":"J. Retail. Consum. Serv."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"123694","DOI":"10.1016\/j.jclepro.2020.123694","article-title":"Pricing Strategies and Profit Coordination Under a Double Echelon Green Supply Chain","volume":"278","author":"Li","year":"2021","journal-title":"J. Clean. Prod."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/TEM.2021.3053386","article-title":"Revenue models for digital servitization: A Value Capture Framework for Designing, Developing, and Scaling Digital Services","volume":"70","author":"Linde","year":"2021","journal-title":"IEEE Trans. Eng. Manag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1256","DOI":"10.1016\/j.econmod.2011.01.008","article-title":"Competition under manufacturer service and retail price","volume":"28","author":"Lu","year":"2011","journal-title":"Econ. Model."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.omega.2018.08.004","article-title":"Optimal pricing in mass customization supply chains with risk-averse agents and retail competition","volume":"88","author":"Choi","year":"2019","journal-title":"Omega"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"103483","DOI":"10.1016\/j.jretconser.2023.103483","article-title":"Pricing coordination of a dual-channel supply chain considering offline in-sale service","volume":"75","author":"Gu","year":"2023","journal-title":"J. Retail. Consum. Serv."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"9","DOI":"10.2753\/MIS0742-1222280301","article-title":"Value chain linkages and the spillover effects of strategic information technology alignment: A process-level view","volume":"28","author":"Tallon","year":"2011","journal-title":"J. Manag. Inf. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1016\/j.ejor.2020.09.003","article-title":"Quality Differentiation in a Dual-Channel Supply Chain","volume":"290","author":"Zhang","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"4359","DOI":"10.1049\/gtd2.12973","article-title":"Multi-Stage Stochastic Dual Dynamic Programming to Low-Carbon Economic Dispatch for Power Systems with Flexible Carbon Capture and Storage Devices","volume":"17","author":"Zhang","year":"2023","journal-title":"Iet Gener. Transm. 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