Computing maximum proportion and most violated sets

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Mehdi Ghiyasvand Mehdi Ghiyasvand

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF OPERATIONS RESEARCH Year:2022 | Volume:13 | Issue:1 Page(s): 123-134

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Information Journal Paper

Title

Computing maximum proportion and most violated sets

Author(s)

Mehdi Ghiyasvand Mehdi Ghiyasvand | Issue Writer Certificate

Keywords

The market equilibrium problem

Fisher's and Arrow-Debreu's models

Violated sets

Abstract

In Fisher's and Arrow-Debreu's market equilibrium models with linear utilities, a set B of buyers and a set G of divisible goods, suppose that there are some buyers with surplus money w.r.t current prices of goods. If there does not exists an equilibrium, then, there are some buyers with surplus money w.r.t the given prices. A set of buyers with surplus money called a violated set. Computing this set helps to find the set of buyers with maximum surplus money w.r.t the given prices. In this paper, two new kinds of Violated sets are defined, which called maximum proportion and most Violated sets. We present an algorithm to compute a maximum proportion set, which runs in at most |B| maximum flow computations. Also, we show that the set of all buyers B is a most violated set.

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