Carbon trading downstream, as a key strategy for decreasing carbon emissions, has the potential to hasten the entire society's decarbonization. Taking the government, household, and carbon trading management center as stakeholders, this paper constructs a tripartite evolutionary game model, examines and stimulates evolutionary stability strategies, and then proposes some policy implications. Findings show that the downstream carbon market faces a complex evolutionary process. The promotion of the policy can be split into two periods: policy promotion and policy stability implementation. And proper household size management is a crucial and effective strategy to encourage downstream carbon trading programs and emission reduction.