We extend the analysis of Kiyotaki and Wright, who study an economy in which the different commodities that serve as media of exchange are determined endogenously. Kiyotaki and Wright consider only symmetric, steady-state, pure-strategy equilibria, and find that for some parameter values no such equilibria exist. We consider mixed-strategy equilibria and dynamic equilibria. We prove that a steady-state equilibrium exists for all parameter values and that the number of steady-state equilibria is generically finite. We also show, however, that there may be a continuum of dynamic equilibria. Further, some dynamic equilibria display cycles.

Our goal is to provide a theoretical framework in which both positive and normative aspects of international currency can be addressed in a systematic way. To this end, we use the framework of random matching games and develop a two country model of the world economy, in which two national fiat currencies compete and may be circulated as media of exchange. There are multiple equilibria, which differ in the areas of circulation of the two currencies. In one equilibrium, the two national currencies are circulated only locally. In another, one of the national currencies is circulated as an international currency. There is also an equilibrium in which both currencies are accepted internationally. We also find an equilibrium in which the two currencies are directly exchanged. The existence conditions of these equilibria are characterized, using the relative country size and the degree of economic integration as the key parameters. In order to generate sharper predictions in the presence of multiple equilibria, we discuss an evolutionary approach to equilibrium selection, which is used to explain the evolution of the international currency as the two economies become more integrated. Some welfare implications are also discussed. For example, a country can improve its national welfare by letting its own currency circulated internationally, provided the domestic circulation is controlled for. When the total supply is fixed, however, a resulting currency shortage may reduce the national welfare.