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Main Authors: Dubey, Pradeep, Sahi, Siddhartha, Shubik, Martin
Format: Preprint
Published: 2015
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Online Access:https://arxiv.org/abs/1512.04637
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author Dubey, Pradeep
Sahi, Siddhartha
Shubik, Martin
author_facet Dubey, Pradeep
Sahi, Siddhartha
Shubik, Martin
contents Consider an exchange mechanism which accepts diversified offers of various commodities and redistributes everything it receives. We impose certain conditions of fairness and convenience on such a mechanism and show that it admits unique prices, which equalize the value of offers and returns for each individual. We next define the complexity of a mechanism in terms of certain integers $τ_{ij},π_{ij}$ and $k_{i}$ that 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, in each of which all trade is conducted through markets for commodity pairs. Finally we consider minimal mechanisms with smallest worst-case complexities $τ=\maxτ_{ij}$ and $π=\maxπ_{ij}$. 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 $m\rightarrow \infty$ the money mechanism is the only one with bounded $\left( π,τ\right) $.
format Preprint
id arxiv_https___arxiv_org_abs_1512_04637
institution arXiv
publishDate 2015
record_format arxiv
spellingShingle Graphical Exchange Mechanisms
Dubey, Pradeep
Sahi, Siddhartha
Shubik, Martin
Computer Science and Game Theory
Theoretical Economics
Combinatorics
91B64
Consider an exchange mechanism which accepts diversified offers of various commodities and redistributes everything it receives. We impose certain conditions of fairness and convenience on such a mechanism and show that it admits unique prices, which equalize the value of offers and returns for each individual. We next define the complexity of a mechanism in terms of certain integers $τ_{ij},π_{ij}$ and $k_{i}$ that 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, in each of which all trade is conducted through markets for commodity pairs. Finally we consider minimal mechanisms with smallest worst-case complexities $τ=\maxτ_{ij}$ and $π=\maxπ_{ij}$. 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 $m\rightarrow \infty$ the money mechanism is the only one with bounded $\left( π,τ\right) $.
title Graphical Exchange Mechanisms
topic Computer Science and Game Theory
Theoretical Economics
Combinatorics
91B64
url https://arxiv.org/abs/1512.04637