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Improved Algorithms for Computing Fisher's Market Clearing Prices

Author James B. Orlin

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  • Market equilibrium
  • Fisher
  • strongly polynomial

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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.

Cite As Get BibTex

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

Author Details

James B. Orlin
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