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arXiv · 1607.04710

A Descending Price Auction for Matching Markets

Shih-Tang Su·Jacob D. Abernethy·Grant Schoenebeck·Vijay G. Subramanian
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Abstract

This work presents a descending-price-auction algorithm to obtain the maximum market-clearing price vector (MCP) in unit-demand matching markets with m items by exploiting the combinatorial structure. With a shrewd choice of goods for which the prices are reduced in each step, the algorithm only uses the combinatorial structure, which avoids solving LPs and enjoys a strongly polynomial runtime of $O(m^4)$. Critical to the algorithm is determining the set of under-demanded goods for which we reduce the prices simultaneously in each step of the algorithm. This we accomplish by choosing the subset of goods that maximize a skewness function, which makes the bipartite graph series converges to the combinatorial structure at the maximum MCP in $O(m^2)$ steps. A graph coloring algorithm is proposed to find the set of goods with the maximal skewness value that yields $O(m^4)$ complexity.

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BibTeXRIS

Shih-Tang Su, Jacob D. Abernethy, Grant Schoenebeck, Vijay G. Subramanian. 2016-07-16. A Descending Price Auction for Matching Markets. https://arxiv.org/abs/1607.04710

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