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Random Matching under Dichotomous Preferences

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  • Moulin, Herve

    (Rice U)

  • Bogomolnaia, Anna

    (Southern Methodist U)

Abstract

We consider bilateral matching problems where each person views those on the other side of the market as either acceptable or unacceptable: an acceptable mate is preferred to remaining single, and the latter to an unacceptable mate; all acceptable mates are welfare-wise identical. Using randomization, many efficient and fair matching methods define strategy-proof revelation mechanisms. Randomly selecting a priority ordering of the participants is a simple example. Equalizing as much as possible the probability of getting an acceptable mate across all participants stands out for its normative and incentives properties: the profile of probabilities is Lorenz dominant, and the revelation mechanism is group-strategy-proof for each side of the market. Our results apply to the random assignment problem as well.

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Paper provided by Rice University, Department of Economics in its series Working Papers with number 2001-03.

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Date of creation: Oct 2001
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Handle: RePEc:ecl:riceco:2001-03

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  1. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  2. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  3. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  4. Ehlers, Lars & Klaus, Bettina & Papai, Szilvia, 2002. "Strategy-proofness and population-monotonicity for house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 329-339, November.
  5. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
  6. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
  7. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer, vol. 16(4), pages 557-567.
  8. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer, vol. 21(2), pages 265-280, October.
  9. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
  10. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
  11. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer, vol. 19(2), pages 153-69.
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