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 ).