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Computing maximum proportion and most violated sets
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Mehdi Ghiyasvand *    |
| Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran , mghiyasvand@basu.ac.ir |
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Abstract: (497 Views) |
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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| Keywords: The market equilibrium problem, Fisher's and Arrow-Debreu's models, Violated sets |
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Full-Text [PDF 545 kb]
(1897 Downloads)
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Type of Study: Original |
Subject:
Mathematical Modeling and Applications of OR
Received: 2023/04/20 | Accepted: 2022/05/30 | Published: 2022/05/30
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