A　virtual　power　plant　(VPP)　has　the　ability　to　aggregate　numerous　decentralized　distributed　energy　resources　using　advanced　control　technology,　offering　a　promising　approach　for　low-carbon　development.　In　order　to　enhance　the　VPP’s　contribution　to　reducing　carbon　emissions,　a　bi-level　framework　is　proposed　that　incorporates　an　integrated　energy-carbon　price　response　mechanism.　This　model　allows　VPPs　to　participate　in　a　multi-energy　system　through　a　multi-agent　Stackelberg　game　framework.　Initially,　a　transaction　model　is　established　where　the　power　distribution　system　operator　and　the　gas　distribution　system　operator　act　as　leaders,　while　the　virtual　power　plant　operator　acts　as　a　follower　in　the　multi-energy　system.　Subsequently,　an　integrated　energy-carbon　pricing　method,　rooted　in　carbon　emission　flow　theory,　is　introduced　to　encourage　VPPs　to　proactively　adjust　their　energy-use　and　trading　strategies　within　multi-energy　systems,　thereby　promoting　multi-principal　interactive　trading.　To　achieve　a　distributed　solution　among　multiple　entities　while　maintaining　the　privacy　of　each　entity’s　information,　the　adaptive　step-size　alternating　direction　multiplier　method　is　employed.　The　feasibility　and　effectiveness　of　the　proposed　model　and　method　are　then　demonstrated　through　case　studies.　Copyright　©　2024　Yan,　Xie,　Tang,　Qian,　Lin　and　Zhang.