This paper focuses on an ex post trading problem in inter-bank money markets. An "over the counter" inter-bank market is modeled in this paper. Relationship banking leads to private proprietary information that causes bargaining failure in such markets with positive probability. Both independent and interdependent bargaining games are studied. It is shown that the allocation is not constrained efficient under bargaining games without monetary intervention. Monetary intervention is characterized as state contingent market making by the Central Bank. Such intervention is shown to dominate under a variety of informational and bargaining assumptions. The literature on monetary policy design is thus extended in the present paper by providing a micro-rationale for Central Bank intervention and by characterizing the solution of state contingent market making in liquidity.