This paper proposes a carbon emission allowance (CEA) bargaining model for prosumers in regional energy networks. The model is designed to enable cost-effective decarbonization by integrating intra-regional CEA sharing and integration. Game theory is introduced to construct a multi-agent CEA bargaining model, which is solved using the alternating direction multiplier method (ADMM) to consider competitive burden and privacy preservation. The upper-level model formulates a carbon flow-led nodal carbon price based on the carbon emission flow (CEF) technique, while the lower-level model focuses on CEA trading among prosumers, converted into cooperative alliance maximization and benefit distribution subproblems. Numerical results demonstrate that the proposed model significantly reduces regional carbon emissions and improves the economic benefits of prosumers. The model's effectiveness is validated through a case study using the E30G20-3P system, showing that CEA bargaining leads to more stable and credible transaction prices and reduces total costs for prosumers. The ADMM algorithm efficiently solves the model, with the number of iterations and calculation time remaining manageable even with multiple prosumers.This paper proposes a carbon emission allowance (CEA) bargaining model for prosumers in regional energy networks. The model is designed to enable cost-effective decarbonization by integrating intra-regional CEA sharing and integration. Game theory is introduced to construct a multi-agent CEA bargaining model, which is solved using the alternating direction multiplier method (ADMM) to consider competitive burden and privacy preservation. The upper-level model formulates a carbon flow-led nodal carbon price based on the carbon emission flow (CEF) technique, while the lower-level model focuses on CEA trading among prosumers, converted into cooperative alliance maximization and benefit distribution subproblems. Numerical results demonstrate that the proposed model significantly reduces regional carbon emissions and improves the economic benefits of prosumers. The model's effectiveness is validated through a case study using the E30G20-3P system, showing that CEA bargaining leads to more stable and credible transaction prices and reduces total costs for prosumers. The ADMM algorithm efficiently solves the model, with the number of iterations and calculation time remaining manageable even with multiple prosumers.