The Emissions Trading System (ETS) is a market-oriented policy aimed at regulating and diminishing greenhouse gas emissions by allocating and trading carbon allowances. Previous studies have mainly focused on dynamic model simulations, while the overall equilibrium state of ETS systems has yet to be explored. To this end, this paper proposes an empirical agent-based model to analyse European carbon allowance auctions: Within the ETS framework, energy companies adopt different strategies to interact in the primary carbon auction market. We use two different methods: partial equilibrium analysis and role-symmetric game analysis to simplify the model strategy space. We then apply the \(\alpha \) -rank algorithm to determine the model’s equilibrium strategy and conduct an in-depth analysis of the combination of these strategies. We examine carbon output levels under these conditions and find that the ETS framework effectively reduces carbon emissions across the system. We also explore the impact of different simplification methods and auction formats on the ETS market: Our results indicate that role-symmetric game analysis has better payoff performance; in addition, uniform auctions improve production efficiency, while discriminatory auctions successfully allocate resources, leading to fairer market competition.