This study introduces a novel bargaining solution termed the ”min-distance bargaining solution” and applies it to a differential games model. A comprehensive algorithm for implementing this new solution is presented, considering its time consistency within the differential games framework. Realistic scenarios are carefully analyzed to derive insightful findings regarding the min-distance solution, which are further validated through simulations using the resource extraction differential games model. Specifically, we examine scenarios such as managing a finite resource stock in the resource extraction game. Furthermore, a comparative analysis is conducted, pitting the min-distance bargaining solution against well-established alternatives such as Nash bargaining, Kalai-Smorodinsky, and Egalitarian solutions. By subjecting these solutions to numerical evaluations, the study offers valuable insights into decision-making processes. The findings not only contribute to negotiation theory by providing theoretical support but also have practical implications for decision-makers seeking effective strategies. This research significantly advances the field of negotiation theory, particularly in the context of differential games. The proposed min-distance bargaining solution demonstrates its applicability to real-world scenarios and enhances our understanding of strategic decision-making.