Asymmetric Nash Bargaining Compensation Mechanism With Individual Limited Budgets for Minimum Cost Consensus in Social Network

In green supply chain initiatives, small suppliers often struggle to achieve collaborative adjustment goals due to limited budgets, even when overall resources are sufficient. This reflects a common challenge in group decision making (GDM) under individual budget constraints. To address this, a novel framework is proposed for achieving group consensus in social networks with limited individual budgets. First, the minimum cost consensus model (MCCM) is extended by introducing a budget relaxation method to explore the potential of Pareto improvement when strict budget constraints hinder consensus. To realize this potential, an asymmetric Nash bargaining cost allocation model with compensation factors is developed to fairly distribute consensus costs within individual budgets. On this basis, an asymmetric Nash bargaining compensation mechanism in ego-networks is designed, reflecting the reality that in decentralized decision-making scenarios, compensation typically occurs among directly connected individuals due to stronger trust, more frequent interactions, and shared interests. This mechanism enables DM to negotiate and reallocate resources within their local social circles, balancing individual and collective benefits and enhancing the feasibility of cooperation. The effectiveness of the proposed framework is demonstrated through an illustrative example.