IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v329y2026i2p556-576.html

Cost management with default risk in large-scale group decision making: A method based on cooperative bargaining game

Author

Listed:
  • Li, Yulong
  • Wang, Zhuang
  • Shen, Yinghua
  • Pedrycz, Witold

Abstract

The collective ranking of alternatives with high consensus is the core and ultimate goal of large-scale group decision making (LSGDM). However, the involvement of a large number of decision makers (DMs) with diverse status or expertise poses challenges for cost management. Fair and rational analysis of cost management considering default risk is necessary but lacking in the current LSGDM research. We view the consensus reaching process (CRP) as a bargaining process where subgroup spokesmen (SSs) will compensate the decision-modification costs of DMs. Based on cooperative bargaining, a novel cost management method for LSGDM considering default risk is developed in this paper. First, we define alternative ranking models for DMs and introduce two modes for adjusting the ranking of alternatives according to high and low default risk, respectively. Then, a series of cost management models is developed to determine the upper and lower bounds of DM’s compensation cost under these two risk scenarios. Subsequently, based on the Kalai-Smorodinsky bargaining solution, we analyze the bargaining power of SSs and DMs in the CRP process and highlight the managerial implications. We find that the bargaining power of DMs and SSs stems from their possession of "resources" that the other needs, either to confer benefits or to inflict costs. The fair and rational compensation cost considering default risk are then determined. Finally, we demonstrate the effectiveness and applicability of the cost management method through the comprehensive experimental study. The results indicate that a small amount of compensation for default risk, combined with the fair and rational analysis considering the bargaining power of DMs and SSs, can significantly control DMs’ default risk below the specified threshold. Our method not only theoretically contributes to the cost management research, but also provides managerial insights for LSGDM organizers to determine fair and rational compensation scheme considering default risk of DMs.

Suggested Citation

  • Li, Yulong & Wang, Zhuang & Shen, Yinghua & Pedrycz, Witold, 2026. "Cost management with default risk in large-scale group decision making: A method based on cooperative bargaining game," European Journal of Operational Research, Elsevier, vol. 329(2), pages 556-576.
    • Handle: RePEc:eee:ejores:v:329:y:2026:i:2:p:556-576
    DOI: 10.1016/j.ejor.2025.07.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221725005727
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2025.07.047?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    2. Gong, Zaiwu & Xu, Xiaoxia & Zhang, Huanhuan & Aytun Ozturk, U. & Herrera-Viedma, Enrique & Xu, Chao, 2015. "The consensus models with interval preference opinions and their economic interpretation," Omega, Elsevier, vol. 55(C), pages 81-90.
    3. Gong, Zaiwu & Zhang, Huanhuan & Forrest, Jeffrey & Li, Lianshui & Xu, Xiaoxia, 2015. "Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual," European Journal of Operational Research, Elsevier, vol. 240(1), pages 183-192.
    4. Alfredo Altuzarra & José María Moreno-Jiménez & Manuel Salvador, 2010. "Consensus Building in AHP-Group Decision Making: A Bayesian Approach," Operations Research, INFORMS, vol. 58(6), pages 1755-1773, December.
    5. Li, Huanhuan & Ji, Ying & Ding, Jieyu & Qu, Shaojian & Zhang, Huijie & Li, Yuanming & Liu, Yubing, 2024. "Robust two-stage optimization consensus models with uncertain costs," European Journal of Operational Research, Elsevier, vol. 317(3), pages 977-1002.
    6. Li, Yanhong & Kou, Gang & Li, Guangxu & Peng, Yi, 2022. "Consensus reaching process in large-scale group decision making based on bounded confidence and social network," European Journal of Operational Research, Elsevier, vol. 303(2), pages 790-802.
    7. Meng, Fan-Yong & Gong, Zai-Wu & Pedrycz, Witold & Chu, Jun-Fei, 2023. "Selfish-dilemma consensus analysis for group decision making in the perspective of cooperative game theory," European Journal of Operational Research, Elsevier, vol. 308(1), pages 290-305.
    8. Chao, Xiangrui & Kou, Gang & Peng, Yi & Viedma, Enrique Herrera, 2021. "Large-scale group decision-making with non-cooperative behaviors and heterogeneous preferences: An application in financial inclusion," European Journal of Operational Research, Elsevier, vol. 288(1), pages 271-293.
    9. Fanyong Meng & Zijun Li & Zongrun Wang, 2023. "Cooperative game theory based consistency and consensus reaching process for group decision making with fuzzy preference relations," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 74(10), pages 2261-2276, October.
    10. Jie Tang & Fanyong Meng, 2024. "An Adaptive Core-Nash Bargaining Game Consensus Mechanism for Group Decision Making," Group Decision and Negotiation, Springer, vol. 33(4), pages 805-837, August.
    11. Zhang, Bowen & Dong, Yucheng & Zhang, Hengjie & Pedrycz, Witold, 2020. "Consensus mechanism with maximum-return modifications and minimum-cost feedback: A perspective of game theory," European Journal of Operational Research, Elsevier, vol. 287(2), pages 546-559.
    12. Tang, Ming & Liao, Huchang, 2021. "From conventional group decision making to large-scale group decision making: What are the challenges and how to meet them in big data era? A state-of-the-art survey," Omega, Elsevier, vol. 100(C).
    13. Shen, Yufeng & Ma, Xueling & Kou, Gang & Rodríguez, Rosa M. & Zhan, Jianming, 2025. "Consensus methods with Nash and Kalai–Smorodinsky bargaining game for large-scale group decision-making," European Journal of Operational Research, Elsevier, vol. 321(3), pages 865-883.
    14. Gong, Zaiwu & Guo, Weiwei & Herrera-Viedma, Enrique & Gong, Zejun & Wei, Guo, 2020. "Consistency and consensus modeling of linear uncertain preference relations," European Journal of Operational Research, Elsevier, vol. 283(1), pages 290-307.
    15. Meng, Fanyong & Tang, Jie & An, Qingxian, 2023. "Cooperative game based two-stage consensus adjustment mechanism for large-scale group decision making," Omega, Elsevier, vol. 117(C).
    16. Liu, Bingsheng & Zhou, Qi & Ding, Ru-Xi & Palomares, Iván & Herrera, Francisco, 2019. "Large-scale group decision making model based on social network analysis: Trust relationship-based conflict detection and elimination," European Journal of Operational Research, Elsevier, vol. 275(2), pages 737-754.
    17. Cheng, Dong & Zhou, Zhili & Cheng, Faxin & Zhou, Yanfang & Xie, Yujing, 2018. "Modeling the minimum cost consensus problem in an asymmetric costs context," European Journal of Operational Research, Elsevier, vol. 270(3), pages 1122-1137.
    18. Cheng, Dong & Yuan, Yuxiang & Wu, Yong & Hao, Tiantian & Cheng, Faxin, 2022. "Maximum satisfaction consensus with budget constraints considering individual tolerance and compromise limit behaviors," European Journal of Operational Research, Elsevier, vol. 297(1), pages 221-238.
    19. Ming Tang & Huchang Liao & Xiaomei Mi & Xuanhua Xu & Francisco Herrera, 2021. "Dynamic subgroup-quality-based consensus in managing consistency, nearness, and evenness quality indices for large-scale group decision making under hesitant environment," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(4), pages 865-878, March.
    20. Wade D. Cook & Moshe Kress, 1985. "Ordinal Ranking with Intensity of Preference," Management Science, INFORMS, vol. 31(1), pages 26-32, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shen, Yufeng & Ma, Xueling & Kou, Gang & Rodríguez, Rosa M. & Zhan, Jianming, 2025. "Consensus methods with Nash and Kalai–Smorodinsky bargaining game for large-scale group decision-making," European Journal of Operational Research, Elsevier, vol. 321(3), pages 865-883.
    2. Ding, Ru-Xi & Yang, Bing & Huang, Yibo & Zhang, Yankai & Chiclana, Francisco, 2026. "Social network-based overlapping community clustering and feedback mechanism for large-scale group decision making," European Journal of Operational Research, Elsevier, vol. 329(2), pages 518-535.
    3. Lang, Ningning & Wang, Lin & Zha, Quanbo, 2026. "Network game in group decision making: Managing consensus with incentive and interaction interventions," European Journal of Operational Research, Elsevier, vol. 329(3), pages 950-965.
    4. Tang, Jie & Li, Zi-Jun & Meng, Fan-Yong & Gong, Zai-Wu & Pedrycz, Witold, 2025. "Biform game consensus analysis of group decision making with unconnected social network," European Journal of Operational Research, Elsevier, vol. 324(1), pages 259-275.
    5. Gong, Zaiwu & Guo, Weiwei & Słowiński, Roman, 2021. "Transaction and interaction behavior-based consensus model and its application to optimal carbon emission reduction," Omega, Elsevier, vol. 104(C).
    6. Meng, Fan-Yong & Zhao, Deng-Yu & Gong, Zai-Wu & Chu, Jun-Fei & Pedrycz, Witold & Yuan, Zhe, 2024. "Consensus adjustment for multi-attribute group decision making based on cross-allocation," European Journal of Operational Research, Elsevier, vol. 318(1), pages 200-216.
    7. Meng, Fan-Yong & Gong, Zai-Wu & Pedrycz, Witold & Chu, Jun-Fei, 2023. "Selfish-dilemma consensus analysis for group decision making in the perspective of cooperative game theory," European Journal of Operational Research, Elsevier, vol. 308(1), pages 290-305.
    8. Zhang, Hengjie & Dong, Yucheng & Chiclana, Francisco & Yu, Shui, 2019. "Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design," European Journal of Operational Research, Elsevier, vol. 275(2), pages 580-598.
    9. Cheng, Dong & Yuan, Yuxiang & Wu, Yong & Hao, Tiantian & Cheng, Faxin, 2022. "Maximum satisfaction consensus with budget constraints considering individual tolerance and compromise limit behaviors," European Journal of Operational Research, Elsevier, vol. 297(1), pages 221-238.
    10. Guo, Weiwei & Gong, Zaiwu & Zhang, Wei-Guo & Xu, Yanxin, 2023. "Minimum cost consensus modeling under dynamic feedback regulation mechanism considering consensus principle and tolerance level," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1279-1295.
    11. Xu, Yuan & Liu, Shifeng & Cheng, T.C.E. & Feng, Xue & Wang, Jun & Shang, Xiaopu, 2025. "Opinion convergence and management: Opinion dynamics in interactive group decision-making," European Journal of Operational Research, Elsevier, vol. 323(3), pages 938-951.
    12. Xiangrui Chao & Yucheng Dong & Gang Kou & Yi Peng, 2022. "How to determine the consensus threshold in group decision making: a method based on efficiency benchmark using benefit and cost insight," Annals of Operations Research, Springer, vol. 316(1), pages 143-177, September.
    13. Siqi Zhang & Jianjun Zhu, 2025. "Conflict Elimination Mechanism in Group Decision-Making Guided by Quantum-Integrated Personalized Risk Attitudes," Group Decision and Negotiation, Springer, vol. 34(5), pages 993-1034, October.
    14. Yifan Ma & Ying Ji, 2026. "A Combinational Consensus Model-Based Feedback Mechanism for Group Decision-Making with Uncertain Adjustment Costs," Group Decision and Negotiation, Springer, vol. 35(1), pages 1-31, March.
    15. Du, Junliang & Liu, Sifeng & Liu, Yong, 2022. "A limited cost consensus approach with fairness concern and its application," European Journal of Operational Research, Elsevier, vol. 298(1), pages 261-275.
    16. Zhang, Siqi & Zhu, Jianjun, 2025. "Eliminating conflicts in group decision-making: Exploring potential information cocoon effects across varied levels of psychological resilience," European Journal of Operational Research, Elsevier, vol. 326(3), pages 544-557.
    17. Kai Zhu & Shaojian Qu & Ying Ji & Yifan Ma, 2025. "Distributionally Robust Chance Constrained Maximum Expert Consensus Model with Incomplete Information on Uncertain Cost," Group Decision and Negotiation, Springer, vol. 34(1), pages 135-175, February.
    18. Dong Cheng & Huina Zhang & Yong Wu, 2025. "Maximum expert consensus models with both type- $$\alpha $$ and type- $$\varepsilon $$ constraints," Journal of Combinatorial Optimization, Springer, vol. 50(2), pages 1-23, September.
    19. Wang, Peng & Liu, Peide & Li, Yueyuan & Teng, Fei & Pedrycz, Witold, 2024. "Trust exploration- and leadership incubation- based opinion dynamics model for social network group decision-making: A quantum theory perspective," European Journal of Operational Research, Elsevier, vol. 317(1), pages 156-170.
    20. Tang, Ming & Liao, Huchang, 2024. "Group efficiency and individual fairness tradeoff in making wise decisions," Omega, Elsevier, vol. 124(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:329:y:2026:i:2:p:556-576. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.