Fiat exchange in finite economies

The state of the art of rendering fiat money valuable is either to impose a boundary condition or to make the boundary condition unimportant through an infinite sequence of markets so as to circumvent backward induction. We show fiat exchange may nevertheless arise in finite economies if agents have incomplete information about their relative position in the trade cycle or when the barter and autarky equilibria of the one-shot trading round support a monetary equilibrium with repeated trades.