We examine the theoretical properties of the auction for Medicare Durable Medical Equipment. Two unique features of the Medicare auction are (1) winners are paid the median winning bid and (2) bids are nonbinding. We show that median pricing results in allocation inefficiencies as some high‐cost firms potentially displace low‐cost firms as winners. Further, the auction may leave demand unfulfilled as some winners refuse to supply because the price is set below their cost. We also introduce a model of nonbinding bids that establishes the rationality of a lowball bid strategy employed by many bidders in the actual Medicare auctions and recently replicated in Caltech experiments. We contrast the median‐price auction with the standard clearing‐price auction where each firm bids true costs as a dominant strategy, resulting in competitive equilibrium prices and full efficiency. (JEL D44, I11, H57)