On the international scene, away from national legal rules, the use of different currencies is largely due to the operation of the 'Invisible Hand'. The paper develops a three-country model of the world economy and links real trade patterns with currency exchange structures in a general equilibrium framework which includes transaction costs on foreign exchange markets. In the presence of strategic complementarities, there are multiple equilibrium structures of currency exchange for a given underlying real trade pattern. The existence conditions of these different equilibria are characterised, using the trade links between countries as the key parameters. Finally, repercussions of the choice of a currency exchange structure on world output are analysed.