This paper offers a game theoretic model of liquidity provision through repeated central bank tenders, in the spirit of the operational framework of the Eurosystem. Banks are required to satisfy reserve requirements subject to an averaging provision over individual maintenance periods, and transactions may hang over into the respective subsequent period. It is shown that liquidity shocks are absorbed by the system by exponentially declining oscillations around the stationary equilibrium. When a policy rate cut is expected, bidders strategically reduce demand prior to the decision, which may unbalance the system. The anticipation of strategic behavior may generate an oscillation even before the maintenance period in which the decision is expected. When the recently released ECB proposal is implemented in the model, then the bidders' strategic motives are effectively eliminated. It is shown that, alternatively, bidding behavior can be corrected using a simple reimbursement scheme.