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Random assignment of multiple indivisible objects

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  • Kojima, Fuhito

Abstract

We consider random assignment of multiple indivisible objects. When each agent receives one object, [Bogomolnaia, A., Moulin, H., 2001. A new solution to the random assignment problem. Journal of Economic Theory 100, 295-328] show that the probabilistic serial mechanism is ordinally efficient, envy-free and weakly strategy-proof. When each agent receives more than one object, we propose a generalized probabilistic serial mechanism that is ordinally efficient and envy-free but not weakly strategy-proof. Our main result shows that, if each agent receives more than one object, there exists no mechanism that is ordinally efficient, envy-free and weakly strategy-proof.

Suggested Citation

  • Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
  • Handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:134-142
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    References listed on IDEAS

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    1. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
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    10. Yan Chen & Tayfun Sönmez, 2002. "Improving Efficiency of On-Campus Housing: An Experimental Study," American Economic Review, American Economic Association, vol. 92(5), pages 1669-1686, December.
    11. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May.
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    Citations

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    Cited by:

    1. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    2. Onur Kesten & Morimitsu Kurino & Alexander S. Nesterov, 2017. "Efficient lottery design," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 31-57, January.
    3. Jörgen Kratz, 2017. "Overlapping multiple object assignments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 723-753, March.
    4. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 203-215, June.
    5. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    6. Thanh Nguyen & Ahmad Peivandi & Rakesh Vohra, 2014. "One-Sided Matching with Limited Complementarities," PIER Working Paper Archive 14-030, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. Carroll, Gabriel, 2014. "A general equivalence theorem for allocation of indivisible objects," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 163-177.
    8. repec:eee:matsoc:v:90:y:2017:i:c:p:80-92 is not listed on IDEAS
    9. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    10. Özgün Ekici & Onur Kesten, 2016. "An equilibrium analysis of the probabilistic serial mechanism," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 655-674, August.
    11. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    12. repec:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1059-3 is not listed on IDEAS
    13. Diebold, Franz & Bichler, Martin, 2017. "Matching with indifferences: A comparison of algorithms in the context of course allocation," European Journal of Operational Research, Elsevier, vol. 260(1), pages 268-282.
    14. repec:eee:matsoc:v:90:y:2017:i:c:p:56-62 is not listed on IDEAS
    15. Eun Jeong Heo & Vikram Manjunath, 2017. "Implementation in stochastic dominance Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 5-30, January.
    16. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.

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