A simplistic model of the emergence of money

We present a simplistic model of the competition between dierent currencies. Each individual is free to choose the currency that minimizes his transaction costs, which arise whenever his exchanging relations have chosen a dierent currency. We show that competition between currencies does not necessarily converge to the emergence of a single currency. For large systems, we prove that two distinct communities using dier-ent currencies in the initial state will remain forever in this fractionalized state.