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• This paper proposes a bi-level Stackelberg low-carbon economic dispatch model with reward and penalty stepped carbon trading mechanism, horizontal and vertical integrated demand response, and dynamic supply and demand multi-energy pricing. • This paper also provides a multi-angle sensitivity analysis of the impact of different parameters of the stepped carbon trading mechanism on the operation of the CIES. • An innovative analysis of the impact of single and two-factor carbon interval length, carbon growth rate, and carbon base price on the CIES is presented. • The sensitivity analysis of horizontal integrated demand response is also carried out. • Through horizontal and vertical integrated demand response, the dynamic supply and demand multi-energy pricing of CIES is further improved. To solve the problem of coupled and coordinated dispatch of multi-energy between campus integrated energy system operator and users. A bi-level Stackelberg low-carbon economic dispatch model with horizontal and vertical integrated demand response and dynamic supply and demand multi-energy pricing (DSDMEP) is proposed. Firstly, the DSDMEP is established to effectively coordinate the interests of the upper CIESO and lower users. Secondly, the combined heat and power containing the power to gas and carbon capture system and the reward and penalty stepped carbon trading mechanism (SCTM) are introduced on the energy supply side to minimize carbon emissions. Then, the HVIDR is introduced to the users to increase the energy coupling and adjustable price characteristics of supply and demand. Finally, the results show that the proposed model compared to other scenarios has its carbon emissions reduced by 21.72%, the benefits of CIESO are increased by 27.86%, and the cost of the users is reduced by 6.9%. This paper also provides a multi-angle sensitivity analysis of the impact of different parameters of the SCTM on the operation of the campus integrated energy system (CIES), as well as a sensitivity analysis of the HVIDR and peak and valley electricity price difference. [ABSTRACT FROM AUTHOR]