Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2015
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1512.04637 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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) $.