The researchers explored different ways to understand bargaining solutions without perfect fairness. They looked at how these solutions can apply to different preferences beyond what we expect. They built on previous work to explain these solutions for situations where the outcomes don't have to be equal between players. By doing this, they found a way to connect the results of similar situations, even if they aren't exactly the same. This work gives us new insights into how bargaining can work in situations where fairness isn't the only goal.