Title: Bidirectional optimised auction model for carbon emission rights with incremental reserve price strategy

Authors: Zenghua Du; Hongren Yan; Sheng Yang; ZhiGuo Hu

Addresses: School of Economics and Management, North University of China, Taiyuan, 030051, Shanxi, China ' School of Computer and Information Technology, Shanxi University, Taiyuan, 030051, Shanxi, China ' School of Computer and Information Technology, Shanxi University, Taiyuan, 030051, Shanxi, China ' School of Computer and Information Technology, Shanxi University, Taiyuan, 030051, Shanxi, China

Abstract: Carbon emission trading has become a widely adopted and effective strategy for mitigating greenhouse gas emissions. Among the various trading mechanisms, auction-based models have demonstrated superior efficiency in allocating emission allowances. However, existing studies primarily emphasise revenue maximisation, often overlooking the critical role of the seller's reserve price. This paper argues that incorporating a reserve price not only safeguards the seller's interests but also incentivises buyers to engage in energy conservation and emission reduction efforts. We propose a novel multi-stage auction model that jointly optimises the revenues of both sellers and buyers across multiple bidding rounds, incorporating seller-defined, non-decreasing reserve price functions. Theoretical analysis confirms the correctness and convergence of the model, and illustrative examples are provided to demonstrate its practical applicability. Compared to existing approaches, our model offers a more realistic and balanced framework by explicitly considering the impact of dynamic reserve pricing on the benefits of both parties, thereby aligning more closely with the operational needs of carbon auction markets.

Keywords: carbon emission right; auction model; non-decreasing; reserve price functions; Vickrey-Clarke-groves; bi-directional optimisation; maximum revenue; theoretical interpretation.

DOI: 10.1504/IJCSM.2025.151194

International Journal of Computing Science and Mathematics, 2025 Vol.22 No.3, pp.227 - 246

Received: 20 Aug 2024
Accepted: 25 Jul 2025
Published online: 16 Jan 2026 *

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