Strategy-proof matching with regional minimum quotas

Masahiro Goto, Naoyuki Hashimoto, Atshushi Iwasaki, Yujiro Kawasaki, Suguru Ueda, Yosuke Yasuda, Makoto Yokoo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Citations (Scopus)

Abstract

This paper considers the matching problem with regional quotas, in particular, regional minimum quotas. Although such quotas are relevant in many real-world settings, there is a lack of strategy-proof mechanisms that consider regional minimum quotas. We first show that without any restrictions on the region structure, finding a feasible matching that satisfies all quotas is NP-complete. Then, assuming that regions have a hierarchical structure (in this case, a tree), and maximum quotas are imposed only on individual schools, we show that checking the existence of a feasible matching can be done in a linear time in the number of regions. Furthermore, we develop strategy-proof matching mechanisms based on the Deferred Acceptance mechanism (DA), which we call Multi-Stage DA with Regional minimum Quotas (MSDA-RQ) and Round-robin Selection DA with Regional minimum Quotas (RSDA-RQ). When minimum quotas are imposed, fairness and nonwastefulness are incompatible. We prove that RSDA-RQ is fair but wasteful, while MSDA-RQ is nonwasteful but not fair. Moreover, we compare our mechanisms with artificial cap mechanisms whose individual maximum quotas are adjusted beforehand so that all regional quotas can be automatically satisfied. Our simulation reveals that our mechanisms substantially outperform artificial cap mechanisms in terms of student welfare. Furthermore, it illustrates the trade-off between our mechanisms.

Original languageEnglish
Title of host publication13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages1225-1232
Number of pages8
ISBN (Electronic)9781634391313
Publication statusPublished - Jan 1 2014
Event13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014 - Paris, France
Duration: May 5 2014May 9 2014

Publication series

Name13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014
Volume2

Other

Other13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014
CountryFrance
CityParis
Period5/5/145/9/14

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence

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  • Cite this

    Goto, M., Hashimoto, N., Iwasaki, A., Kawasaki, Y., Ueda, S., Yasuda, Y., & Yokoo, M. (2014). Strategy-proof matching with regional minimum quotas. In 13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014 (pp. 1225-1232). (13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014; Vol. 2). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).