Two-sided strategy-proofness in many-to-many matching markets
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Two-sided strategy-proofness in many-to-many matching markets Antonio Romero-Medina1
· Matteo Triossi2
Accepted: 11 October 2020 © The Author(s) 2020
Abstract We study the existence of group strategy-proof stable rules in many-to-many matching markets under responsiveness of agents’ preferences. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proof rule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof mechanisms in many-to-many matching markets. Keywords Many-to-many · Acyclicity · Stability · Strategy-proofness Mathematics Subject Classification C71 · C78 · D71
1 Introduction Many real-world markets are many-to-many. The canonical example of a many-tomany market is the specialty training followed by junior doctors in the UK (Roth 1991). Other examples of many-to-many markets are markets for part-time workers and the non-exclusive dealings between down-stream firms and up-stream providers. Many-to-many markets are also useful to model multi-unit assignment problems such
We thank the associate editor and the two reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. Both authors acknowledge financial support from Ministerio Economía y Competitividad (Spain) under project ECO2017-87769-P and from Fondecyt under project No. 1151230. Romero-Medina acknowledges the financial support from Ministerio Economía y Competitividad (Spain) MDM 2014-0431, and Comunidad de Madrid H2019/HUM-5891. Triossi acknowledges the financial support from the Institute for Research in Market Imperfections and Public Policy, ICM IS130002, Ministerio de Economía, Fomento y Turismo (Chile), and from Ca’ Foscari University of Venice under project MAN.INS_TRIOSSI.
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Matteo Triossi [email protected]
1
Department of Economics, Universidad Carlos III de Madrid, Madrid, Spain
2
Department of Management, Ca’ Foscari University of Venice, Venice, Italy
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A. Romero-Medina and M. Triossi
as course allocations (see Budish 2011; Sönmez and Ünver 2010; Kojima 2013) or the assignment of landing slots (see Schummer and Vohra 2013; Schummer and Abizada 2017). We consider a many-to-many matching market and assume that preferences are responsive (Roth 1985). Under this assumption, no mechanism is stable and strategyproof for even one side of the market (see Roth and Sotomayor 1990). Furthermore, even in one-to-one markets, there is no mechanism that is stable and strategy-proof for the agents on both sides of the market. Due to these negative results, the literature has concentrated on mechanisms guaranteeing strategy-proofness on one side of the market, thus overlooking preference manipulation from agents on the other side of the market (but see Romero-Medina and Triossi 2013a for capacity manipulation). However, manipulation by agents on both sides of the market is a concern, for ex
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