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Allocation via Deferred-Acceptance under Responsive Priorities

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  • EHLERS, Lars
  • KLAUS, Bettina

Abstract

In many economic environments - such as college admissions, student placements at public schools, and university housing allocation - indivisible objects with capacity constraints are assigned to a set of agents when each agent receives at most one object and monetary compensations are not allowed. In these important applications the agent-proposing deferred-acceptance algorithm with responsive priorities (called responsive DA-rule) performs well and economists have successfully implemented responsive DA-rules or slight variants thereof. First, for house allocation problems we characterize the class of responsive DA-rules by a set of basic and intuitive properties, namely, unavailable type invariance, individual rationality, weak non-wastefulness, resource-monotonicity, truncation invariance, and strategy-proofness. We extend this characterization to the full class of allocation problems with capacity constraints by replacing resource-monotonicity with two-agent consistent conflict resolution. An alternative characterization of responsive DA-rules is obtained using unassigned objects invariance, individual rationality, weak non-wastefulness, weak consistency, and strategy-proofness. Various characterizations of the class of "acyclic" responsive DA-rules are obtained by using the properties eciency, group strategy-proofness, and consistency.

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 17-2009.

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Length: 27 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:mtl:montec:17-2009

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Keywords: consistency; deferred-acceptance algorithm; indivisible objects allocation; resourcemonotonicity; strategy-proofness; weak non-wastefulness;

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  1. Lars Ehlers & Bettina Klaus, 2002. "Efficient Priority Rules," UFAE and IAE Working Papers 554.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Lars Ehlers & Bettina Klaus, 2007. "Consistent House Allocation," Economic Theory, Springer, vol. 30(3), pages 561-574, March.
  3. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer, vol. 36(3), pages 537-569, March.
  4. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  5. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  6. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
  7. Bettina Klaus & Lars Ehlers, 2009. "Corrigendum to "Resource-Monotonicity for House Allocation Problems"," Harvard Business School Working Papers 09-110, Harvard Business School.
  8. Lars Ehlers & Bettina Klaus, 2003. "Resource-Monotonicity for House Allocation," Working Papers 33, Barcelona Graduate School of Economics.
  9. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
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