The carbon market has been playing an increasingly important role in mitigating carbon emissions. However, with the tightening of the carbon allowance, where the carbon market will evolve is still unclear. Abstracting three agents—Government, Carbon-supplier(‘CS’), Carbon-buyer(‘CB’), this paper intends to investigate the operation mechanism of carbon market from the perspective of the stakeholders. Based on the simulation analysis, it is suggested that: 1) the carbon market in China may become a major “seller's market” when carbon quota experienced dramatic reduction; 2) when the carbon price is constant, CS with excessive carbon productivity will crowd out and exploit CB in the carbon market competition; 3) strict administrative penalties and information disclosure would help promote proactive participation of CS and CB in the carbon market; and 4) the interaction between CS and CB in different strategic scenarios is influenced by the carbon price and the coefficient of demand variation for carbon quota. In contrast with previous studies, this paper has uncovered a dynamic strategic evolution mechanisms of stakeholders in the carbon market at the micro-level, contributing to carbon market governance and providing stakeholders with tailor-made climate policy tools and strategic choices. •The carbon market in China may evolve into a “seller's market” with a scarcer allowance.•We first identify the phenomenon of carbon exploitation in the carbon market.•Improving the carbon price under buyer's market would facilitate positive participation of three agents.•Carbon accounting, carbon disclosure, and strict administrative penalty help regulate non-compliance actions by enterprises.•The equilibrium of agents' strategy are influenced by dual aspects—parameters and other stakeholders' choices.