A Theory of Monetary Exchange - Norman, Alfred Lorn (Review of Economic Studies, 1987)
The transactions cost for alternative exchange mechanisms for the household exchange problem can be characterized by the computational complexity of the exchange process. The computational complexity for any exchange mechanism is at least nH, where n is the number of goods and H is the number of households. Imposing the conditions of conservation, nonnegativity and quid pro quo results in a command exchange mechanism whose computational complexity is nH. Multiparty barter exchange, formalized using graph theory, has computational complexity equal to the minimum of (nH2, n2H). Introducing an auxiliary good, money, reduces the computational complexity to nH. A problem with decentralized information is demonstrated.