Approximate tradeoffs on weighted labeled matroids

We consider problems where a solution is evaluated with a couple. Each coordinate of this couple represents the utility of an agent. Due to the possible conflicts, it is unlikely that one feasible solution is optimal for both agents. Then a natural aim is to find a tradeoff. We investigate tradeoff solutions with worst case guarantees for the agents. The focus is on discrete problems having a matroid structure and the utility of an agent is modeled with a function which is either additive or weighted labeled. We provide polynomial-time deterministic algorithms which achieve several guarantees and we prove that some guarantees are not possible to reach.