Nowadays,　the　rapid　development　of　intelligent　navigation　systems　has　profound　impacts　on　the　routing　of　traffic　users.　With　the　assistance　of　these　intelligent　navigation　systems,　traffic　users　can　obtain　more　accurate　information　about　a　traffic　network　such　as　traffic　capacities,　feasible　paths,　congestion　status,　etc.　In　this　paper,　we　focus　on　a　game-theory-based　traffic　congestion　analysis　model　which　considers　incomplete　traffic　information　(e.g.,　variabilities　of　path　information)　generated　by　intelligent　navigation　systems.　The　variabilities　of　path　information　are　treated　as　incomplete　information　associated　with　different　subsets　of　arcs.　We　adopt　the　notions　of　user　equilibrium　with　incomplete　information　(UEII)　and　system　optimum　with　incomplete　information　(SOII)　in　this　study.　Based　on　these　two　new　notions,　we　extend　two　classical　theorems　and　combine　them　into　a　new　model　to　analyze　the　relationship　between　UEII　and　SOII.　Finally,　numerical　cases　are　given　to　illustrate　the　implication　of　UEII　and　SOII　in　practical　implementations.　©　2020,　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.