Dynamic searchable symmetric encryption (SSE) enables clients to update and search encrypted data stored on a server and provides efficient search operations instead of leakages of inconsequential information. Towards dynamic SSE for more practical situations, researchers have tackled research on multi-user dynamic SSE (dynamic MUSE for short), sometimes with flexible access control. However, existing schemes assumed a trusted authority that played a crucial role during the search protocol, used pairings/lattices for their constructions, or provided no security proofs. In this paper, we show the first dynamic MUSE scheme with reasonable access control without the above limitations. Namely, our dynamic MUSE model requires no trusted authority, and our concrete dynamic MUSE scheme with prefix-fixing predicates, which yields a reasonable, hierarchical access control, can be constructed from only symmetric-key primitives and with rigorous security proof. Our experimental results show that our dynamic MUSE scheme is reasonably efficient.