In a simple search model of money, we study a special kind of memory that gives rise to an arrangement resembling a payment network. Specifically, we assume that agents can pay a cost to access a central database that tracks payments made and received. Incentives must be provided to agents to access the central database and to produce when they participate in this arrangement. We also study policies that can loosen these incentive constraints. In particular, we show that a “no-surcharge” rule has good incentive properties. Finally, we compare our model with that of Cavalcanti and Wallace.