Pradeep Dubey, Siddhartha Sahi, Martin Shubik

Paper #: 14-05-012

We consider exchange mechanisms that accept “diversified” offers of commodities and redistribute everything. Under certain natural conditions of “fairness” and “convenience”, we show that such mechanisms admit unique prices that equalize the value of offers and returns for each individual.

We next define the complexity of a mechanism in terms of integers τij, πij and ki which represent the “time”required to exchange i for j, the “difficulty” in determining the exchange ratio, and the “dimension”of the message space. We show that there are a finite number of minimally complex mechanisms; and, in each, all trade is conducted through markets for commodity pairs.

Finally we consider minimal mechanisms, with smallest “worst case”complexities τ = max τij and π = max πij. For m > 3 commodities, there are precisely three such mechanisms, one of which has a distinguished commodity — the money — that serves as the sole medium of exchange. As m → ∞ the money mechanism is the only one with bounded (π, τ ).