It is widely acknowledged that verifying the safety of autonomous driving strategies requires a substantial body of simulation testing and road testing. In recent years, the formal safety methods represented by Responsibility-Sensitive Safety (RSS) have encouraged low-cost autonomous driving safety research, benefitting from its accurate assessment of safety and clear division of responsibilities. However, how to maintain traffic efficiency while ensuring safety remains a challenge. To address this problem, this paper proposes a formulized negotiation-based lane-changing strategy that makes a trade-off between safety and efficiency. Both theoretical analysis and numerical experimental results shows that compared to RSS, our strategy can noticeably improve the success rate of changing lanes on the premise of safety.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.