Money as Minimal Complexity
Pradeep Dubey, Siddhartha Sahi, Martin Shubik

TL;DR
This paper characterizes minimal complexity mechanisms for commodity exchange, showing that the star mechanism with money is uniquely optimal in terms of trade efficiency and information requirements for large commodity sets.
Contribution
It introduces a formal framework for measuring the complexity of exchange mechanisms and proves the star mechanism's optimality among minimal structures for large commodity sets.
Findings
The star, cycle, and complete graph mechanisms are the only minimal structures for m>3.
The star mechanism uniquely minimizes a weighted sum of complexity measures for large m.
The star mechanism uses money as the sole medium of exchange, simplifying trade processes.
Abstract
We consider mechanisms that provide traders the opportunity to exchange commodity for commodity , for certain ordered pairs . Given any connected graph of opportunities, we show that there is a unique mechanism that satisfies some natural conditions of "fairness" and "convenience". Let denote the class of mechanisms obtained by varying on the commodity set . We define the complexity of a mechanism in to be a certain pair of integers which represent the time required to exchange for and the information needed to determine the exchange ratio (each in the worst case scenario, across all ). This induces a quasiorder on by the rule \[ M\preceq M^{\prime}\text{if}\tau(M)\leq\tau(M^{\prime})\text{and}\pi(M)\leq\pi(M^{\prime}). \]…
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Taxonomy
TopicsEconomic theories and models · Economic Theory and Institutions · Game Theory and Applications
