A Game-Based Two-Stage Competition-Cooperation Consensus Model for Large-Scale Multi-Attribute Group Decision Making

Feng Wang () and Xiaobing Yu ()
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Feng Wang: Nanjing University of Information Science and Technology
Xiaobing Yu: Nanjing University of Information Science and Technology

Group Decision and Negotiation, 2025, vol. 34, issue 6, No 4, 1327-1370

Abstract: Abstract With increasingly complex issues, group decision-making (GDM) is gradually extended to large-scale multi-attribute GDM. It is much more difficult to reach a consensus in large-scale GDM than in GDM. To cope with this challenge, this paper proposes a two-stage consensus modification method based on game theory. First, an adaptive clustering algorithm is designed to decompose the large group into multiple subgroups. Then, subgroup weight is calculated according to the internal and external characteristics of the subgroup. Based on the trust and consensus degree of each DM within the subgroup, Data Envelopment Analysis is adopted to determine DM weights. In the first stage, we establish a bi-level programming model from the perspective of Stackelberg game, which is solved by designing an intelligence algorithm. In the second stage, we apply the cooperative game theory to rationally allocate the modification amount to DMs in the subgroup. To do this, we construct the Shapley value of individual consensus modification. Based on the allocation scheme, we build a minimum modification consensus model to determine all modified opinions from a holistic angle. Finally, a case study is provided to illustrate the proposed decision-making process. Meanwhile, a sensitivity analysis and comparison analysis validate its effectiveness.

Keywords: Large; Scale multi; Attribute group decision; Making; Consensus model; Modification amount; Stackelberg game; Cooperative game (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10726-025-09948-7

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