Developing　an　efficient,　cost-effective　and　environmentally　friendly　waste　management　mode　remains　a　major　challenge　for　municipalities.　The　classification　and　recycling　of　municipal　household　waste　(MHW)　is　a　complex　system　with　multiple　interacting　agents.　This　study　presents　a　tripartite　evolutionary　game　(EG)　analysis　of　MHW　classification　and　recycling,　consisting　of　local　governments,　enterprises,　and　urban　residents.　We　analyzed　the　stability　of　the　inter-agents　based　on　their　behavior　strategies.　To　achieve　the　optimal　status　of　the　EG　model,　we　designed　the　learning　strategy　and　imitation　mechanism　of　the　agent　using　stochastic　disturbance　terms　based　on　bounded　rationality.　Our　simulation　results　suggest　that　the　EG　model　above　achieved　the　stability　of　the　optimal　strategy　when　the　following　conditions　were　satisfied:　(1)　the　MHW　classification　income　of　urban　residents　was　higher　than　their　classification　cost;　(2)　the　comprehensive　supervision　income　of　local　government　was　greater　than　its　supervision　cost.　From　the　perspective　of　specific　behavioral　strategy　influencing　factors,　urban　residents　are　more　prone　to　change　decisions　under　positive　government　incentives　than　enterprises,　however,　the　behavioral　decisions　of　enterprises　are　primarily　affected　by　government　penalties.　In　the　early　phase,　it　is　important　to　improve　the　convenience　of　MHW　classification　and　recycling　and　increase　the　income　of　urban　residents　to　foster　proper　waste　sorting　and　recycling　habits.　The　findings　of　this　study　can　be　used　to　strengthen　efforts　towards　the　achievement　of　the　urban　sustainable　development　goals　related　to　MHW.