DagSemProc.10171.2.pdf
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Improved Algorithms for Computing Fisher's Market Clearing Prices
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Dagstuhl Seminar Proceedings, Volume 10171
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2010-07-15
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James B. Orlin. Improved Algorithms for Computing Fisher's Market Clearing Prices. In Equilibrium Computation. Dagstuhl Seminar Proceedings, Volume 10171, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/DagSemProc.10171.2
https://doi.org/10.4230/DagSemProc.10171.2
Abstract
We give the first strongly polynomial time algorithm for computing
an equilibrium for the linear utilities case of Fisher's market model.
We consider a problem with a set $B$ of buyers and a set $G$ of divisible goods.
Each buyer $i$ starts with an initial integral allocation
$e_i$ of money. The integral utility for buyer $i$ of
good $j$ is $U_{ij}$. We first develop a weakly polynomial
time algorithm that runs in $O(n^4 log U_{max} + n^3 e_{max})$ time, where
$n = |B| + |G|$. We further modify the algorithm so that it runs
in $O(n^4 log n)$ time. These algorithms improve upon the
previous best running time of
$O(n^8 log U_{max} + n^7 log e_{max})$, due to Devanur et al.
Keywords
- Market equilibrium
- Fisher
- strongly polynomial
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