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Abstract People have long been trading in a “monetary” way. This persistence of monetary trading suggests that it might be an efficient trading mechanism. We formalize this intuition in a random-matching, absence-of-double-coincidence-of-wants environment. The record-keeping technology is operated by an information-processing center which summarizes and updates individuals’ past trading behavior in a binary variable. A trading mechanism consists of an updating rule and an individual trading behavior rule. To capture the difficulties in collecting and processing information about others’ past behavior, we assume that the center faces costs, both fixed and variable, to operate. We show that (1) any non-autarkic equilibrium trading mechanism is, in terms of aggregate variables (such as consumption and frequency of trade), observationally equivalent to a monetary trading mechanism and (2) any non-autarkic optimal equilibrium trading mechanism is a monetary trading mechanism.