Within the context of the global "dual-carbon" policy, the study explores the low-carbon energy transactions among diverse entities in the comprehensive energy market and the constraints imposed by the design of tiered carbon tax policies. This has emerged as a research hotspot in the field of low-carbon economic dispatch. The paper comprehensively examines the coupled relationship between the energy consumption and corresponding carbon emission factors among four entities: microgrid energy operators, flexible shared energy storage, electric to heat transfer operator, and community aggregator. It maps the corresponding energy prices into the interests of a non-cooperative game among entities, thereby guiding each entity to achieve a balance between carbon emissions and economic costs. The paper utilizes an enhanced genetic-particle swarm hybrid algorithm for solving and validates the effectiveness of the dispatch strategy by analyzing the marginal and cumulative effects generated by the design of tiered carbon tax policies. The findings indicate that under continuous tiered carbon tax mapping, the formulation strategy of electricity and heat prices has been further optimized, balancing the interests of the four entities, and effectively enhancing the integration of new energy while reducing the output of fossil energy units.