Abstract There are two alternative methods of supporting interbank exchange of payments: payment exchange may be supported by a direct presentment regulation, which obligates a paying bank to make payment in full to whomever delivers the payment instrument to it; alternatively the interbank exchange of payments may be governed by private contracts. Examples of the two cases are provided in the U.S. by cheques, which are subject to direct presentment regulations, and credit cards and debit cards, which are governed by private contracts. A model in which the interchange fee charged by banks under a collective agreement to clear payments can be used as an instrument of tacit collusion, is examined. However, under direct presentment, the equilibrium fee, for a range of the parameter set, is set to zero. At the same time, because, under direct presentment, it is difficult to exclude banks from issuing payments, banks have incentives to impede the collection of payments. One way they can do so is through the strategy of remote disbursement, in which banks intentionally delay payments. A collectively-owned entity, or a public one, that quickly presents cheques to the banks engaging in the remote presentment strategy can work to overcome the incentives to remotely present the cheques, but at a resource cost. Assuming a monopoly multilateral agreement for the privately contracted payment instrument, the interchange fee specified by the contract is an instrument of tacit collusion and can in some circumstances support the monopoly outcome. However, it avoids the problem of attempts to impede payments. These results naturally lead to an exploration of whether direct presentment regulations should be changed, so that all payment instruments that transfer bank liabilities can be governed by private contract. L51, L16, L9.