I explore the estimation of transferable utility matching games, encompassing many‐to‐many matching, marriage, and matching with trading networks (trades). Computational issues are paramount. I introduce a matching maximum score estimator that does not suffer from a computational curse of dimensionality in the number of agents in a matching market. I apply the estimator to data on the car parts supplied by automotive suppliers to estimate the valuations from different portfolios of parts to suppliers and automotive assemblers.