Article 6 of the Paris Agreement enables Parties to achieve their Nationally Determined Contributions (NDCs) through direct cooperation or Internationally Transferred Mitigation Outcomes (ITMO). Current researches on Article 6 are mostly based on the assumption of unlimited global carbon market link, which may lead to large price volatility and cause concern of policy makers. In order to investigate the impact of inter-regional carbon market link mechanism on global climate action, here, we designed carbon market link scenarios with different degrees of trading volume limits. We simulated the global and regional carbon markets under different scenarios from 2025 to 2060 using the Global Change Assessment Model (GCAM). The findings suggest that as the link limit tightens, both the price volatility of global carbon market and the cumulative mitigation costs saved by carbon market links decrease, which reminds policy makers of the trade-off between economic efficiency and price volatility. The price volatility under the unlimited global carbon market scenario is about 30% higher than that with link limits implemented, while the unlimited market would also save about 0.83 trillion dollars abatement costs than the limited scenario. At the national level, a total of 14 regions are limited in different link limit scenarios, among which China, the United States, EU and India are the most sensitive regions to link limits. Based on the scenario results, we discuss the design of international carbon market link mechanisms, such as absolute link limits and relative link limits. • A trade-off between economic efficiency and price volatility under link limit. • A total of 14 regions are limited in the limit scenarios. • China, U.S., EU and India are the most sensitive regions to link limits. • Regional heterogeneity in sensitivity to absolute and relative limit mechanisms. • The direction of the financial flows remains unchanged with link limits. [ABSTRACT FROM AUTHOR]