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| Main Authors: | , , |
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| Format: | Preprint |
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2015
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1512.04637 |
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| _version_ | 1866912038081527808 |
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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 |