Using detailed transactions‐level data on interbank loans, we examine the efficiency of an overnight interbank lending market and the bargaining power of its participants. Our analysis relies on the equilibrium concept of the core, which imposes a set of no‐arbitrage conditions on trades in the market. For Canada's Large Value Transfer System, we show that although the market is fairly efficient, systemic inefficiency persists throughout our sample. The level of inefficiency matches distinct phases of both the Bank of Canada's operations as well as phases of the 2007–8 financial crisis. We find that bargaining power tilted sharply toward borrowers as the financial crisis progressed and (surprisingly) toward riskier borrowers.