On money as a medium of exchange

We analyze economies in which individuals specialize in consump-tion and production and meet randomly over time in a way that implies that trade must be bilateral and quid pro quo. Nash equilib-ria in trading strategies are characterized. Certain goods emerge endogenously as media of exchange, or commodity money, depend-ing both on their intrinsic properties and on extrinsic beliefs. There are also equilibria with genuine fiat currency circulating as the gen-eral medium of exchange. We find that equilibria are not generally Pareto optimal and that introducing fiat currency into a commodity money economy may unambiguously improve welfare. Velocity, ac-ceptability, and liquidity are discussed.