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Non-Revelation Mechanisms for Many-to-Many Matching: Equilibria versus Stability

Listed author(s):
  • Bettina Klaus
  • Flip Klijn

We study many-to-many matching markets in which agents from a set A are matched to agents from a disjoint set B through a two-stage non-revelation mechanism. In the first stage, A-agents, who are endowed with a quota that describes the maximal number of agents they can be matched to, simultaneously make proposals to the B-agents. In the second stage,B-agents sequentially, and respecting the quota, choose and match to available A-proposers. We study the subgame perfect Nash equilibria of the induced game. We prove that stable matchings are equilibrium outcomes if all A-agents' preferences are substitutable. We also show that the implementation of the set of stable matchings is closely related to the quotas of the A-agents. In particular, implementation holds when A-agents' preferences are substitutable and their quotas are non-binding.

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File URL: http://hec.unil.ch/attachments/deep/series/2016/16.07.pdf
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Paper provided by Université de Lausanne, Faculté des HEC, DEEP in its series Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) with number 16.07.

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Length: 12 pp.
Date of creation: Apr 2016
Handle: RePEc:lau:crdeep:16.07
Contact details of provider: Postal:
Université de Lausanne, Faculté des HEC, DEEP, Internef, CH-1015 Lausanne

Phone: ++41 21 692.33.20
Web page: http://www.hec.unil.ch/deep/publications/cahiers/series
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  1. Vulkan, Nir & Roth, Alvin E. & Neeman, Zvika (ed.), 2013. "The Handbook of Market Design," OUP Catalogue, Oxford University Press, number 9780199570515.
  2. Alcalde, Jose & Romero-Medina, Antonio, 2000. "Simple Mechanisms to Implement the Core of College Admissions Problems," Games and Economic Behavior, Elsevier, vol. 31(2), pages 294-302, May.
  3. Romero Medina, Antonio & Triossi, Matteo, 2017. "Take-it-or-leave-it contracts in many-to-many matching markets," UC3M Working papers. Economics 24368, Universidad Carlos III de Madrid. Departamento de Economía.
  4. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
  5. Marilda Sotomayor, 2003. "Reaching the core of the marriage market through a non-revelation matching mechanism," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 241-251, December.
  6. Romero-Medina, Antonio & Triossi, Matteo, 2014. "Non-revelation mechanisms in many-to-one markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 624-630.
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