Money and credit in random matching models of money

I review in this paper some recent literature that deals with the coexistence of inside and outside money in a matching model of money à la Kiyotaki and Wright. I examine first a class of models that introduce credit by assuming that some agents’ actions can be monitored and punished by the other agents in the economy. I then turn to a model in which agents can (costly) commit to keep their promises. I also analyse a literature that introduces banks and private money in the model, to evaluate the Hayek-Friedman debate on the private vs. public provision of money. The very last part of the paper is devoted to the issue of coexistence of money and nominal bonds with a higher rate of return.