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House allocation with fractional endowments

Author

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  • Stergios Athanassoglou

    ()

  • Jay Sethuraman

    ()

Abstract

This paper studies a generalization of the well known house allocation problem in which agents may own fractions of different houses summing to an arbitrary quantity, but have use for only the equivalent of one unit of a house. It departs from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. For this general model, an algorithm is designed to find a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. The analysis extend to the full preference domain. Individual rationality, ordinal efficiency, and no justified envy conflict with weak strategyproofness. Moreover, individual rationality, ordinal efficiency and strategyproofness are shown to be incompatible. Finally, two reasonable notions of envy-freeness, no justified envy and equal-endowment no envy, conflict in the presence of ordinal efficiency and individual rationality. All of the impossibility results hold in the strict preference domain.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Stergios Athanassoglou & Jay Sethuraman, 2011. "House allocation with fractional endowments," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 481-513, August.
  • Handle: RePEc:spr:jogath:v:40:y:2011:i:3:p:481-513
    DOI: 10.1007/s00182-010-0251-9
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. YIlmaz, Özgür, 2009. "Random assignment under weak preferences," Games and Economic Behavior, Elsevier, vol. 66(1), pages 546-558, May.
    5. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    6. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    7. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Han, Xiang, 2016. "On the consistency of random serial dictatorship," Economics Letters, Elsevier, vol. 145(C), pages 168-171.
    2. Kesten, Onur & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    3. 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.
    4. 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.
    5. 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.
    6. Tommy Andersson & Agnes Cseh & Lars Ehlers & Albin Erlanson, 2018. "Organizing Time Banks: Lessons from Matching Markets," IEHAS Discussion Papers 1818, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    7. repec:eee:jetheo:v:170:y:2017:i:c:p:145-168 is not listed on IDEAS
    8. YIlmaz, Özgür, 2009. "Random assignment under weak preferences," Games and Economic Behavior, Elsevier, vol. 66(1), pages 546-558, May.
    9. repec:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1059-3 is not listed on IDEAS
    10. repec:eee:matsoc:v:88:y:2017:i:c:p:3-10 is not listed on IDEAS
    11. Le, Phuong, 2013. "Competitive Equilibrium in the Random Assignment Problem," MPRA Paper 66290, University Library of Munich, Germany.
    12. repec:eee:matsoc:v:90:y:2017:i:c:p:56-62 is not listed on IDEAS
    13. Balbuzanov, Ivan & Kotowski, Maciej H., 2017. "Endowments, Exclusion, and Exchange," Working Paper Series rwp17-016, Harvard University, John F. Kennedy School of Government.
    14. 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.
    15. repec:spr:etbull:v:6:y:2018:i:1:d:10.1007_s40505-017-0122-7 is not listed on IDEAS
    16. repec:bla:ijethy:v:13:y:2017:i:4:p:369-385 is not listed on IDEAS
    17. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Ünver, M. Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    18. Tayfun Sönmez & M. Utku Ünver, 2015. "Enhancing the Efficiency of and Equity in Transplant Organ Allocation via Incentivized Exchange," Boston College Working Papers in Economics 868, Boston College Department of Economics.
    19. Kesten, Onur & Kurino, Morimitsu & Nesterov, Alexander, 2015. "Efficient lottery design," Discussion Papers, Research Unit: Market Behavior SP II 2015-203, WZB Berlin Social Science Center.

    More about this item

    Keywords

    House allocation; Fractional endowments; Fairness; Individual rationality; C72; C78; D71;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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