College Admissions And The Stability Of Marriage Essay

925 Words Jul 8th, 2016 4 Pages
In this paper, a two-sided matching market is considered, and a descending price algorithm based auction mechanism is proposed to determine market clearing prices. For general valuations with an intelligent choice of reverse constricted sets, we prove that the algorithm converges in a finite number of rounds. Then specializing to the rank one valuations in sponsored search markets, we provide an alternate characterization of the set of all market clearing prices, and use this to prove that the proposed algorithm yields the elementwise maximum market clearing price. We then conclude with a a discussion of some special cases and counter-examples in order to get a better understanding of the algorithm.
The problem of matching in markets was first studied by Gale and Shapley in the seminal paper ”College Admissions and the Stability of Marriage” [1]. Soon thereafter a widely used mathematical model of two-sided matching markets was presented in the paper ”The Assignment Game I: The Core” [2] by Shapley and Shubik. The setup consists of a set of sellers and a set of buyers. Each seller comes with one indivisible good and seeks to trade with an unit-demand buyer to earn the most money. During the ensuing decades, the matching market model has been widely studied, and applied to many areas such as commodities trading, matching students to schools, and organization of organ donors. A comprehensive account of the work on this topic can be found in the following surveys [3], [4],…

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