A Newsvendor Non-Cooperative Game for Efficient Allocation of Carbon Emissions

We analytically investigate the impacts of several efficient carbon emissions allocation schemes in a cap-and-trade carbon trading system. Subject to each firm’s allowances restriction, a policy maker accumulates all remaining and exceeding carbon emission allowances over the industry at the end of the accounting year. We develop three new allocation schemes for allocating these total carbon emissions to each firm: Separate Payment (SP), Deterministic Equal Splitting (DES) and Allocation proportion to unit Carbon Emission (ACE). Using a Stackelberg framework based on a newsvendor non-cooperative game, we show that our suggested allocation schemes reduce total carbon emissions by aligning the firms with a single and common objective of “reducing total emissions”, not merely “meeting individual’s allowances”. We characterize the conditions under which SP and DES can equally generate fewer total carbon emissions than ACE. Moreover, we identify the condition in which DES can dominate SP in terms of a firm’s profit while DES and SP generate the same total carbon emissions. Our numerical studies further demonstrate that DES outperforms SP in terms of a firm’s financial performance depending on the gap between the firms’ unit emission rates. This study provides a useful guideline to enhance the firms’ profit while reducing total carbon emissions in the industry.