A Stackelberg-Bayesian Capacity-Market Game of Carbon Regulation and Second-Life Battery Investment under AI Data-Center Load Growth

Abstract

Artificial intelligence (AI) data centers are driving rapid electricity load growth across all U.S. ISO/RTO regions, raising both system costs and carbon exposure. This study develops a three-level Stackelberg--Bayesian game in which a regulator (leader) sets carbon penalties and subsidies, a single ISO capacity market clears against an energy balance modeled as a classical generation-expansion problem, and technology-specific investors (followers) decide capacity and operation under incomplete information, yielding a Bayesian Nash equilibrium. The AI impact is captured parsimoniously as an additional load-growth factor on a greenfield-incremental expansion, isolating how much new capacity the growth pulls in and which technology fills it. Within this framework, we consider second-life battery (SLB) storage competing against new/first-life storage for capacity-market revenue. We quantify how a carbon tax, a renewable subsidy, and an SLB subsidy reshape the equilibrium investment mix, carbon emissions, and profit. Different scenarios are compared at the end based on cost-effectiveness and reduced carbon emissions.