Recent attention has been given to the hypothesis that local hospital competition takes the form of costly duplication of specialized services-the "medical arms race." This contrasts with the hypothesis that the supply of specialized services is determined solely by "the extent of the market." We develop a model predicting the provision of specialized services in local markets. Our analysis of California hospitals provides minimal support for the medical arms race hypothesis while suggesting substantial scale economies for many services. Our results emphasize the importance of properly specifying the extent of the market. Failure to do so leads one to overestimate the importance of competition.