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Improved Algorithms for Computing Fisher's Market Clearing Prices

Author James B. Orlin

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James B. Orlin

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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)


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.
  • Market equilibrium
  • Fisher
  • strongly polynomial


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