Matroid rank valuations

Our paper on Market pricing for matroid rank valuations has been recently accepted for publication in SIAM Journal on Discrete Mathematics. In the paper, we study the problem of maximizing social welfare in combinatorial markets through pricing schemes. We consider the existence of prices that are capable to achieve optimal social welfare without a central tie-breaking coordinator. In the case of two buyers with matroid rank valuations, we give polynomial-time algorithms that always find such prices when one of the matroids is a simple partition matroid, or both matroids are strongly base orderable.