Engineering Design of Matching Markets
Two-sided matching markets under preferences can be described by the stable matching model of Gale and Shapley, proposed for college admissions. Their deferred-acceptance algorithm always produces a student-optimal stable matching in linear time, and it is strategy-proof for the students. Mainly due to these desirable properties, this algorithm has been widely used in many applications across the world, including school choice, college admission, and resident allocation. Yet, having one extra custom feature can turn the corresponding problem intractable in a computational sense, the existence of a fair solution may not be guaranteed any more, and the strategic issues cannot be avoided either. One well-known example for such a market design challenge was the introduction of joint applications by couples in the US resident allocation program. In the 1990s Roth and Peranson managed to successfully resolve the case by taking an engineering approach, and constructing a Gale-Shapley based heuristic algorithm. In this writing we elaborate on this engineering concept by describing further examples for real-life design challenges in matching markets, the related computational and strategic issues, and the possible solution techniques from optimization and game theoretical points of view.
The author acknowledges the support of the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3/2018) and Cooperation of Excellences Grant (KEP-6/2018), and the Hungarian Scientific Research Fund, OTKA, Grant No.\ K128611.
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